Browsing by Author "Kokoszka, Piotr, committee member"
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Item Open Access A measurement of muon neutrino charged-current interactions with a charged pion in the final state using the NOνA near detector(Colorado State University. Libraries, 2023) Rojas, Paul Nelson, author; Buchanan, Norm, advisor; Lee, Siu Au, committee member; Harton, John, committee member; Kokoszka, Piotr, committee memberThe NOνA experiment is a long-baseline neutrino experiment hosted by Fermilab. The intense NuMI neutrino beam, combined with NOνA Near Detector, provides the opportunity to study neutrino interactions at an unprecedented level. The goal of this analysis is to measure the rate of muon-neutrino charged-current interactions in the NOνA near detector resulting in the production of one muon and at least one charged pion. This thesis will present the result of the double differential cross section measurement of this process in muon kinematics of energy and angle. Excesses in the extracted signal (greater than 25%), relative to the simulation, were found at large scattering angles. These excesses were greater than the estimated uncertainties (∼15%).Item Open Access A novel approach to statistical problems without identifiability(Colorado State University. Libraries, 2024) Adams, Addison D., author; Wang, Haonan, advisor; Zhou, Tianjian, advisor; Kokoszka, Piotr, committee member; Shaby, Ben, committee member; Ray, Indrakshi, committee memberIn this dissertation, we propose novel approaches to random coefficient regression (RCR) and the recovery of mixing distributions under nonidentifiable scenarios. The RCR model is an extension of the classical linear regression model that accounts for individual variation by treating the regression coefficients as random variables. A major interest lies in the estimation of the joint probability distribution of these random coefficients based on the observable samples of the outcome variable evaluated for different values of the explanatory variables. In Chapter 2, we consider fixed-design RCR models, under which the coefficient distribution is not identifiable. To tackle the challenges of nonidentifiability, we consider an equivalence class, in which each element is a plausible coefficient distribution that, for each value of the explanatory variables, yields the same distribution for the outcome variable. In particular, we formulate the approximations of the coefficient distributions as a collection of stochastic inverse problems, allowing for a more flexible nonparametric approach with minimal assumptions. An iterative approach is proposed to approximate the elements by incorporating an initial guess of a solution called the global ansatz. We further study its convergence and demonstrate its performance through simulation studies. The proposed approach is applied to a real data set from an acupuncture clinical trial. In Chapter 3, we consider the problem of recovering a mixing distribution, given a component distribution family and observations from a compound distribution. Most existing methods are restricted in scope in that they are developed for certain component distribution families or continuity structures of mixing distributions. We propose a new, flexible nonparametric approach with minimal assumptions. Our proposed method iteratively steps closer to the desired mixing distribution, starting from a user-specified distribution, and we further establish its convergence properties. Simulation studies are conducted to examine the performance of our proposed method. In addition, we demonstrate the utility of our proposed method through its application to two sets of real-world data, including prostate cancer data and Shakespeare's canon word count.Item Open Access Adjusting for capture, recapture, and identity uncertainty when estimating detection probability from capture-recapture surveys(Colorado State University. Libraries, 2015) Edmondson, Stacy L., author; Givens, Geof, advisor; Opsomer, Jean, committee member; Kokoszka, Piotr, committee member; Noon, Barry, committee memberWhen applying capture-recapture analysis methods, estimates of detection probability, and hence abundance estimates, can be biased if individuals of a population are not correctly identified (Creel et. al., 2003). My research, motivated by the 2010 and 2011 surveys of Western Arctic bowhead whales conducted off the shores of Barrow, Alaska, offers two methods for addressing the complex scenario where an individual may be mistaken as another individual from that population, thus creating erroneous recaptures. The first method uses a likelihood weighted capture recapture method to account for three sources of uncertainty in the matching process. I illustrate this approach with a detailed application to the whale data. The second method develops an explicit model for match errors and uses MCMC methods to estimate model parameters. Implementation of this approach must overcome significant hurdles dealing with the enormous number and complexity of potential catch history configurations when matches are uncertain. The performance of this approach is evaluated using a large set of Monte Carlo simulation tests. Results of these test vary from good performance to weak performance, depending on factors including detection probability, number of sightings, and error rates. Finally, this model is applied to a portion of the bowhead survey data and found to produce plausible and scientifically informative results as long as the MCMC algorithm is started at a reasonable point in the space of possible catch history configurations.Item Open Access Applications of least squares penalized spline density estimator(Colorado State University. Libraries, 2024) Jing, Hanxiao, author; Meyer, Mary, advisor; Cooley, Daniel, committee member; Kokoszka, Piotr, committee member; Berger, Joshua, committee memberThe spline-based method stands as one of the most common nonparametric approaches. The work in this dissertation explores three applications of the least squares penalized spline density estimator. Firstly, we present a novel hypothesis test against the unimodality of density functions, based on unimodal and bimodal estimates of the density function, using penalized splines. The test statistic is the difference in the least-squares criterion, between these fits. The distribution of the test statistics under the null hypothesis is estimated via simulated data sets from the unimodal fit. Large sample theory is derived and simulation studies are conducted to compare its performance with other common methods across various scenarios, alongside a real-world application involving neuro-transmission data from guinea pig brains. Secondly, we tackle the deconvolution density estimation problem, introducing the penalized splines deconvolution estimator. Building upon the results gained from piecewise constant splines, we achieve a cube-root convergence rate for piecewise quadratic splines and uniform errors. Moreover, we derive large sample theories for the penalized spline estimator and the constrained spline estimator. Simulation studies illustrate the competitive performance of our estimators compared to the kernel estimators across diverse scenarios. Lastly, drawing inspiration from the preceding applications, we develop a hypothesis test to discern whether the underlying density is unimodal or multimodal, given data with measurement error. Under the assumption of uniform errors, we introduce the test and derive the test statistic. Simulations are conducted to show the performance of the proposed test under different conditions.Item Open Access Detection of a weak radiological source in ambient background using spectral analysis(Colorado State University. Libraries, 2018) Meengs, Matthew Richard, author; Brandl, Alex, advisor; Johnson, Thomas, advisor; Kokoszka, Piotr, committee memberThe detection of radiation requires the use of statistical tools due to the probabilistic nature of the emission and interaction properties of radiation, an analysis that includes the testing of a hypothesis regarding the presence or absence of a source against background. Traditionally, a false positive rate of 5% is used to calculate a y*, the decision threshold, above which a source is determined to be present. However, in radiological conditions where a source is both improbable and weak, and where counting time is limited, detection of a source becomes increasingly challenging using this traditional method. The detection of clandestine fissile materials presents such a challenge, and with the increasing risk of nuclear proliferation, there exists a growing desire to research more optimal methods in detecting these sources, especially where a missed detection is of such high consequence. Previous research has shown that using a string of measurements, and calculating a detection limit based on a certain number of false positives within that string, consistently outperforms the traditional method of basing the detection limit on just one measurement. Such research to date has only been applied to counts of all energies (gross counts). The purpose of this research is to apply the success of this new detection algorithm to certain energies within the spectrum, and to discover whether further optimization is possible by this process. Optimization was evaluated using receiver operator characteristic (ROC) curves, where special emphasis was placed at the lower false positive values. Over the course of this research, two hypothesis were tested. The first hypothesis conjectures that it is indeed possible to further optimize source detection when using an energy bin other than gross counts. The second hypothesis postulates that if the first hypothesis is true, than there exists a mathematical criterion that predicts this behavior. Both hypothesis were verified to be correct.Item Open Access Development of a Bayesian linear regression model for the detection of a weak radiological source from gamma spectra measurements(Colorado State University. Libraries, 2021) Meengs, Matthew, author; Brandl, Alexander, advisor; Johnson, Thomas E., committee member; Sudowe, Ralf, committee member; Kokoszka, Piotr, committee memberThe detection of radiation requires the use of statistical tools due to the probabilistic nature of the emission and the interaction properties of radiation. Frequentist statistical methods are traditionally employed towards this end – the most common being the "traditional" method which calculates a decision threshold above which a source is determined to be present. The decision threshold is calculated from a predetermined false positive rate (typically 5%) and is used as a decision parameter. The decision parameter is a statistical tool by which it is determined whether or not a source other than background is present. In radiological conditions where a source is both improbable and weak, and where counting time is limited, the detection of a source becomes progressively more challenging using this traditional method. The detection of clandestine fissile materials presents such a challenge, and with the increasing risk of nuclear proliferation, there exists a growing motivation to research more optimal methods of detection, especially where a missed detection is of such high consequence. Previous research has been conducted on using a Bayesian model to develop a decision parameter for weak source detection. The use of a Bayesian model has been shown in laboratory settings to outperform the traditional frequentist method. However, the model tested was designed for gross counts only. In the present study, a Bayesian algorithm is being developed and tested that uses the entirety of the gamma spectrum. Specifically, several Bayesian linear regressions are developed and tested which compared different energy ranges in the spectrum. The parameters generated from these linear regressions are tested for their efficacy as decision parameters. With the additional information presented from the entire spectrum, it is theoretically possible that even further improvements in the detection of a weak source can be achieved. The results of this research have shown that regressor coefficients via a Bayesian method are effective as decision parameters. The best results, however, were shown only to match the efficacy of the more traditional, frequentist method of detection.Item Open Access Development of a decision threshold for radiological source detection utilizing Bayesian statistical techniques applied to gross count measurements(Colorado State University. Libraries, 2018) Brogan, John, author; Brandl, Alexander, advisor; Johnson, Thomas E., committee member; Leary, Del, committee member; Kokoszka, Piotr, committee memberNumerous studies have been published using Bayesian statistics in source localization and identification, characterization of radioactive samples, and uncertainty analysis; but there is a limited amount of material specific to the development of a decision threshold for simple gross count measurements using Bayesian statistics. Radiation detection in low fidelity systems is customarily accomplished through the measurement of gross counts. Difficulties arise when applying decision techniques to low count rate data, which are restricted by the fact that decisions are being made on individual gross count measurements alone. The investigation presented demonstrates a method to develop a viable Bayesian model to detect radiological sources using gross count measurements in low fidelity systems. An integral component of the research is the process required to validate a Bayesian model both statistically and operationally in Health Physics. The results describe the necessary model development, validation steps, and application to the detection of radiological sources at low signal-to-background ratios by testing the model against laboratory data. The approach may serve as a guideline for a series of requirements to integrate Bayesian modeling (specifically, an interaction model) with radiation detection using gross counts in low fidelity systems.Item Open Access Improved detection of radioactive material using a series of measurements(Colorado State University. Libraries, 2016) Mann, Jenelle, author; Brandl, Alexander, advisor; Johnson, Thomas, committee member; Kokoszka, Piotr, committee member; Leary, Del, committee memberThe goal of this project is to develop improved algorithms for detection of radioactive sources that have low signal compared to background. The detection of low signal sources is of interest in national security applications where the source may have weak ionizing radiation emissions, is heavily shielded, or the counting time is short (such as portal monitoring). Traditionally to distinguish signal from background the decision threshold (y*) is calculated by taking a long background count and limiting the false negative error (α error) to 5%. Some problems with this method include: background is constantly changing due to natural environmental fluctuations and large amounts of data are being taken as the detector continuously scans that are not utilized. Rather than looking at a single measurement, this work investigates looking at a series of N measurements and develops an appropriate decision threshold for exceeding the decision threshold n times in a series of N. This methodology is investigated for a rectangular, triangular, sinusoidal, Poisson, and Gaussian distribution.Item Open Access Linear prediction and partial tail correlation for extremes(Colorado State University. Libraries, 2022) Lee, Jeongjin, author; Cooley, Daniel, advisor; Kokoszka, Piotr, committee member; Breidt, Jay, committee member; Pezeshki, Ali, committee memberThis dissertation consists of three main studies for extreme value analyses: linear prediction for extremes, uncertainty quantification for predictions, and investigating conditional relationships between variables at their extreme levels. We employ multivariate regular variation to provide a framework for modeling dependence in the upper tail, which is assumed to be a direction of interest. Cooley and Thibaud [2019] consider transformed-linear operations to define a vector space on the nonnegative orthant and show regular variation is preserved by these transformed-linear operations. Extending the approach of Cooley and Thibaud [2019], we first consider the problem of performing prediction when observed values are at extreme levels. This linear approach is motivated by the limitation that traditional extreme value models have difficulties fitting a high dimensional extreme value model. We construct an inner product space of nonnegative random variables from transformed-linear combinations of independent regularly varying random variables. Rather than fully characterizing extremal dependence in high dimensions, we summarize tail behavior via a matrix of pairwise tail dependencies. The projection theorem yields the optimal transformed-linear predictor, which has a similar form to the best linear unbiased predictor in non-extreme prediction. We then quantify uncertainty for the prediction of extremes by using information contained in the tail pairwise dependence matrix. We create the 95% prediction interval based on the geometry of regular variation. We show that the prediction intervals have good coverage in a simulation study as well as in two applications: prediction of high NO2 air pollution levels, and prediction of large financial losses. We also compare prediction intervals with a linear approach to ones with a parametric approach. Lastly, we develop the novel notion of partial tail correlation via projection theorem in the inner product space. Partial tail correlations are the analogue of partial correlations in non-extreme statistics but focus on extremal dependence. Partial tail correlation can be represented by the inner product of prediction errors associated with the previously defined best transformed-linear prediction for extremes. We find a connection between the partial tail correlation and the inverse matrix of tail pairwise dependencies. We then develop a hypothesis test for zero elements in the inverse extremal matrix. We apply the idea of partial tail correlation to assess flood risk in application to extreme river discharges in the upper Danube River basin. We compare the extremal graph constructed from the idea of the partial tail correlation to physical flow connections on the Danube.Item Open Access Modeling the upper tail of the distribution of facial recognition non-match scores(Colorado State University. Libraries, 2016) Hunter, Brett D., author; Cooley, Dan, advisor; Givens, Geof, advisor; Kokoszka, Piotr, committee member; Fosdick, Bailey, committee member; Adams, Henry, committee memberIn facial recognition applications, the upper tail of the distribution of non-match scores is of interest because existing algorithms classify a pair of images as a match if their score exceeds some high quantile of the non-match distribution. I construct a general model for the distribution above the (1-τ)th quantile borrowing ideas from extreme value theory. The resulting distribution can be viewed as a reparameterized generalized Pareto distribution (GPD), but it differs from the traditional GPD in that τ is treated as fixed. Inference for both the (1-τ)th quantile uτ and the GPD scale and shape parameters is performed via M-estimation, where my objective function is a combination of the quantile regression loss function and reparameterized GPD densities. By parameterizing uτ and the GPD parameters in terms of available covariates, understanding of these covariates' influence on the tail of the distribution of non-match scores is attained. A simulation study shows that my method is able to estimate both the set of parameters describing the covariates' influence and high quantiles of the non-match distribution. The simulation study also shows that my model is competitive with quantile regression in estimating high quantiles and that it outperforms quantile regression for extremely high quantiles. I apply my method to a data set of non-match scores and find that covariates such as gender, use of glasses, and age difference have a strong influence on the tail of the non-match distribution.Item Open Access Penalized unimodal spline density estimate with application to M-estimation(Colorado State University. Libraries, 2020) Chen, Xin, author; Meyer, Mary C., advisor; Wang, Haonan, committee member; Kokoszka, Piotr, committee member; Zhou, Wen, committee member; Miao, Hong, committee memberThis dissertation establishes a novel type of robust estimation, Auto-Adaptive M-estimation (AAME), based on a new density estimation. The new robust estimation, AAME, is highly data-driven, without the need of priori of the error distribution. It presents improved performance against fat-tailed or highly-contaminated errors over existing M-estimators, by down-weighting influential outliers automatically. It is shown to be root-n consistent, and has an asymptotically normal sampling distribution which provides asymptotic confidence intervals and the basis of robust prediction intervals. The new density estimation is a penalized unimodal spline density estimation which is established as a basis for AAME. It is constrained to be unimodal, symmetrical, and integrate to 1, and it is penalized to have stabilized derivatives and against over-fitting, overall satisfying the requirements of being applied in AAME. The new density estimation is shown to be consistent, and its optimal asymptotic convergence rate can be obtained when the penalty is asymptotically bounded. We also extend our AAME to linear models with heavy-tailed and dependent errors. The dependency of errors is modeled by an autoregressive process, and parameters are estimated jointly.Item Open Access Statistical innovations for estimating shape characteristics of biological macromolecules in solution using small-angle x-ray scattering data(Colorado State University. Libraries, 2016) Alsaker, Cody, author; Breidt, F. Jay, advisor; Estep, Don, committee member; Kokoszka, Piotr, committee member; Luger, Karolin, committee memberSmall-angle X-ray scattering (SAXS) is a technique that yields low-resolution images of biological macromolecules by exposing a solution containing the molecule to a powerful X-ray beam. The beam scatters when it interacts with the molecule. The intensity of the scattered beam is recorded on a detector plate at various scattering angles, and contains information on structural characteristics of the molecule in solution. In particular, the radius of gyration (Rg) for a molecule, which is a measure of the spread of its mass, can be estimated from the lowest scattering angles of SAXS data using a regression technique known as Guinier analysis. The analysis requires specification of a range or “window” of scattering angles over which the regression relationship holds. We have thus developed methodology and supporting asymptotic theory for selection of an optimal window, minimum mean square error estimation of the radius of gyration, and estimation of its variance. The theory and methodology are developed using a local polynomial model with autoregressive errors. Simulation studies confirm the quality of the asymptotic approximations and the superior performance of the proposed methodology relative to the accepted standard. We show that the algorithm is applicable to data acquired from proteins, nucleic acids and their complexes, and we demonstrate with examples that the algorithm improves the ability to test biological hypotheses. The radius of gyration is a normalized second moment of the pairwise distance distribution p(r), which describes the relative frequency of inter-atomic distances in the structure of the molecule. By extending the theory to fourth moments, we show that a new parameter ψ can be calculated theoretically from p(r) and estimated from experimental SAXS data, using a method that extends Guinier's Rg estimation procedure. This new parameter yields an enhanced ability to use intensity data to distinguish between two molecules with different but similar Rg values. Analysis of existing structures in the protein data bank (PDB) shows that the theoretical ψ values relate closely to the aspect ratio of a molecular structure. The combined values for Rg and ψ acquired from experimental data provide estimates for the dimensions and associated uncertainties for a standard geometric shape, representing the particle in solution. We have chosen the cylinder as the standard shape and show that a simple, automated procedure gives a cylindrical estimate of a particle of interest. The cylindrical estimate in turn yields a good first approximation to the maximum inter-atomic distance in a molecule, Dmax, an important parameter in shape reconstruction. As with estimation of Rg, estimation of ψ requires specification of a window of angles over which to conduct the higher-order Guinier analysis. We again employ a local polynomial model with autoregressive errors to derive methodology and supporting asymptotic theory for selection of an optimal window, minimum mean square error estimation of the aspect ratio, and estimation of its variance. Recent advances in SAXS data collection and more comprehensive data comparisons have resulted in a great need for automated scripts that analyze SAXS data. Our procedures to estimate Rg and ψ can be automated easily and can thus be used for large suites of SAXS data under various experimental conditions, in an objective and reproducible manner. The new methods are applied to 357 SAXS intensity curves arising from a study on the wild type nucleosome core particle and its mutants and their behavior under different experimental conditions. The resulting Rg2 values constitute a dataset which is then analyzed to account for the complex dependence structure induced by the experimental protocols. The analysis yields powerful scientific inferences and insight into better design of SAXS experiments. Finally, we consider a measurement error problem relevant to the estimation of the radius of gyration. In a SAXS experiment, it is standard to obtain intensity curves at different concentrations of the molecule in solution. Concentration-by-angle interactions may be present in such data, and analysis is complicated by the fact that actual concentration levels are unknown, but are measured with some error. We therefore propose a model and estimation procedure that allows estimation of true concentration ratios and concentration-by-angle interactions, without requiring any information about concentration other than that contained in the SAXS data.Item Open Access Toward robust embedded networks in heavy vehicles - machine learning strategies for fault tolerance(Colorado State University. Libraries, 2024) Ghatak, Chandrima, author; Ray, Indrakshi, advisor; Malaiya, Yashwant, committee member; Kokoszka, Piotr, committee memberIn the domain of critical infrastructure, Medium and Heavy Duty (MHD) vehicles play an integral role in both military and civilian operations. These vehicles are essential for the efficiency and reliability of modern logistics. The operations of modern MHD vehicles are heavily automated through embedded computers called Electronic Control Units (ECUs). These ECUs utilize arrays of sensors to control and optimize various vehicle functions and are critical to maintaining operational effectiveness. In most MHD vehicles, this sensor data is predominantly communicated using the Society of Automotive Engineering's (SAE) J1939 Protocol over Controller Area Networks (CAN) and is vital for the smooth functioning of MHD vehicles. The resilience of these communication networks is especially crucial in adversarial environments where sensor systems are susceptible to disruptions caused by physical (kinetic) or cyber-attacks. This dissertation presents an innovative approach using predictive machine learning algorithms to forecast accurate sensor readings in scenarios where sensor systems become compromised. The study focuses on the SAE J1939 networks in MHD vehicles, utilizing real-world data from a Class 6 Kenworth T270 truck. Three distinct machine-learning methods are explored and evaluated for their effectiveness in predicting missing sensor data. The results demonstrate that these models can nearly accurately predict sensor data, which is essential in preventing the vehicle from entering engine protection or limp modes, thereby extending operational capacity under adverse conditions. Overall, this research highlights the potential of machine learning in enhancing the resilience of networked cyber-physical systems, particularly in MHD vehicles. It underscores the significance of predictive algorithms in maintaining operational feasibility and contributes to the broader discussion on the resilience of critical infrastructure in hostile settings.Item Open Access Transformed-linear models for time series extremes(Colorado State University. Libraries, 2022) Mhatre, Nehali, author; Cooley, Daniel, advisor; Kokoszka, Piotr, committee member; Shaby, Benjamin, committee member; Wang, Tianyang, committee memberIn order to capture the dependence in the upper tail of a time series, we develop nonnegative regularly-varying time series models that are constructed similarly to classical non-extreme ARMA models. Rather than fully characterizing tail dependence of the time series, we define the concept of weak tail stationarity which allows us to describe a regularly-varying time series through the tail pairwise dependence function (TPDF) which is a measure of pairwise extremal dependencies. We state consistency requirements among the finite-dimensional collections of the elements of a regularly-varying time series and show that the TPDF's value does not depend on the dimension being considered. So that our models take nonnegative values, we use transformed-linear operations. We show existence and stationarity of these models, and develop their properties such as the model TPDF's. Motivated by investigating conditions conducive to the spread of wildfires, we fit models to hourly windspeed data using a preliminary estimation method and find that the fitted transformed-linear models produce better estimates of upper tail quantities than traditional ARMA models or than classical linear regularly-varying models. The innovations algorithm is a classical recursive algorithm used in time series analysis. We develop an analogous transformed-linear innovations algorithm for our time series models that allows us to perform prediction which is fundamental to any time series analysis. The transformed-linear innovations algorithm also enables us to estimate parameters of the transformed-linear regularly-varying moving average models, thus providing a tool for modeling. We construct an inner product space of transformed-linear combinations of nonnegative regularly-varying random variables and prove its link to a Hilbert space which allows us to employ the projection theorem. We develop the transformed-linear innovations algorithm using the properties of the projection theorem. Turning our attention to the class of MA(∞) models, we talk about estimation and also show that this class of models is dense in the class of possible TPDFs. We also develop an extremes analogue of the classical Wold decomposition. Simulation study shows that our class of models provides adequate models for the GARCH and another model outside our class of models. The transformed-linear innovations algorithm gives us the best prediction and we also develop prediction intervals based on the geometry of regular variation. Simulation study shows that we obtain good coverage rates for prediction errors. We perform modeling and prediction for the hourly windspeed data by applying the innovations algorithm to the estimated TPDF.Item Open Access Weighting adjustments in surveys(Colorado State University. Libraries, 2017) Fu, Ran, author; Opsomer, Jean D., advisor; Breidt, F. Jay, committee member; Kokoszka, Piotr, committee member; Mushinski, David, committee memberWe consider three topics in this dissertation: 1) Nonresponse weighting adjustment using penalized spline regression; 2) Improving survey estimators through weight smoothing; and 3) An investigation of weight smoothing estimators under mixed model specifications. In the first topic, we propose a new survey estimator under nonresponse, which only assumes that the response propensity is a smooth function of a known covariate, and we estimate the propensity function by fitting a nonparametric logistic model using penalized spline regression. We obtain the linearization of the nonresponse weighting adjustment estimator with respect to the sampling design and the random response mechanism, allowing us to perform asymptotically correct inference. In a simulation study, we show that the nonparametric estimator remains competitive with a linear logistic estimator when the response propensity function follows a linear logistic model, but performs significantly better when the response propensity function is nonlinear. Beaumont (2008) proposed model-based weight smoothing as a way to improve the efficiency of survey estimators. In the second topic, we extend this work by obtaining the asymptotic properties of this approach with respect to the sampling design and the weight model. The latter is taken to be a lognormal linear regression model. We derive the asymptotic distribution of the estimator and propose a consistent estimator of the asymptotic variance. A Hájek version of the estimator is considered, as well as a replication variance estimator, both of which improve the robustness of weight smoothing against model misspecification. In the third topic, the results from the second topic are extended to models with random effects. Two versions of the estimator are proposed, depending on whether the random effects are predicted or integrated out, and their practical performance is compared through a simulation study.