Theses and Dissertations  Statistics
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Advances in statistical analysis and modeling of extreme values motivated by atmospheric models and data products
This dissertation presents applied and methodological advances in the statistical analysis and modeling of extreme values. We detail three studies motivated by the types of data found in the atmospheric sciences, such as ... 
Methods for extremes of functional data
Motivated by the problem of extreme behavior of functional data, we develop statistical theory at the nexus of functional data analysis (FDA) and extreme value theory (EVT). A fundamental technique of functional data ... 
Inference for cumulative intraday return curves
The central theme of this dissertation is inference for cumulative intraday return (CIDR) curves computed from high frequency data. Such curves describe how the return on an investment evolves with time over a relatively ... 
Improved inference in heteroskedastic regression models with monotone variance function estimation
The problems associated with heteroskedasticity often lead to incorrect inferences in a regression model, especially when the form of the heteroskedasticity is obscure. In this dissertation, I present methods to estimate ... 
Infinite dimensional Stochastic Inverse Problems
In many disciplines, mathematical models such as differential equations, are used to characterize physical systems. The model induces a complex nonlinear measurable map from the domain of physical parameters to the range ... 
Survey estimators of domain means under shape restrictions
Novel methodologies that introduce shaperestricted regression techniques into survey domain estimation and inference are presented in this dissertation. Although population domain means are frequently expected to respect ... 
Statistical models for dependent trajectories with application to animal movement
In this dissertation, I present novel methodology to study the way animals interact with each other and the landscape they inhabit. I propose two statistical models for dependent trajectories in which depedencies among ... 
Weighting adjustments in surveys
We 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 ... 
Nonparametric tests of spatial isotropy and a calibrationcapturerecapture model
In this dissertation we present applied, theoretical, and methodological advances in the statistical analysis of spatiallyreferenced and capturerecapture data. An important step in modeling spatially referenced data is ... 
Some topics on modelbased clustering
Cluster analysis is widely applied in various areas. Modelbased clustering, which assumes a mixture model, is one of the most useful approaches in clustering. Using modelbased clustering, we can make statistical inferences ... 
Estimation and linear prediction for regression, autoregression and ARMA with infinite variance data
This dissertation is divided into four parts, each of which considers random variables from distributions with regularly varying tails and/or in a stable domain of attraction. Part I considers the existence of infinite ... 
ChangePoint estimation using shaperestricted regression splines
ChangePoint estimation is in need in fields like climate change, signal processing, economics, doseresponse analysis etc, but it has not yet been fully discussed. We consider estimating a regression function ƒm and a ... 
Inference for functional time series with applications to yield curves and intraday cumulative returns
Econometric and financial data often take the form of a functional time series. Examples include yield curves, intraday price curves and term structure curves. Before an attempt is made to statistically model or predict ... 
Modeling the upper tail of the distribution of facial recognition nonmatch scores
In facial recognition applications, the upper tail of the distribution of nonmatch scores is of interest because existing algorithms classify a pair of images as a match if their score exceeds some high quantile of the ... 
Improved estimation and prediction for computationally expensive ecological and paleoclimate models
In this dissertation, we present statistical methods to evaluate estimation and prediction performance for applied ecological problems. We explore a variety of applied problems and, within this context, we investigate how ... 
Statistical innovations for estimating shape characteristics of biological macromolecules in solution using smallangle xray scattering data
Smallangle Xray scattering (SAXS) is a technique that yields lowresolution images of biological macromolecules by exposing a solution containing the molecule to a powerful Xray beam. The beam scatters when it interacts ... 
Penalized isotonic regression and an application in survey sampling
In isotonic regression, the mean function is assumed to be monotone increasing (or de creasing) but otherwise unspecified. The classical isotonic leastsquares estimator is known to be inconsistent at boundaries; this is ... 
Modulated renewal process models with functional predictors for neural connectivities
Recurrent event data arise in fields such as medicine, business and social sciences. In general, there are two types of recurrent event data. One is from a relatively large number of independent processes exhibiting a ... 
Penalized estimation procedure for varying coefficient models, A
Varying coefficient models are widely used for analyzing longitudinal data. Various methods for estimating coefficient functions have been developed over the years. We revisit the problem under the theme of functional ... 
Adjusting for capture, recapture, and identity uncertainty when estimating detection probability from capturerecapture surveys
When applying capturerecapture 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 ...