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Applications of least squares penalized spline density estimator

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dc.contributor.authorJing, Hanxiao, author
dc.contributor.authorMeyer, Mary, advisor
dc.contributor.authorCooley, Daniel, committee member
dc.contributor.authorKokoszka, Piotr, committee member
dc.contributor.authorBerger, Joshua, committee member
dc.date.accessioned2024-09-09T20:52:04Z
dc.date.available2024-09-09T20:52:04Z
dc.date.issued2024
dc.description.abstractThe 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.
dc.format.mediumborn digital
dc.format.mediumdoctoral dissertations
dc.identifierJing_colostate_0053A_18414.pdf
dc.identifier.urihttps://hdl.handle.net/10217/239219
dc.languageEnglish
dc.language.isoeng
dc.publisherColorado State University. Libraries
dc.relation.ispartof2020-
dc.rightsCopyright and other restrictions may apply. User is responsible for compliance with all applicable laws. For information about copyright law, please see https://libguides.colostate.edu/copyright.
dc.titleApplications of least squares penalized spline density estimator
dc.typeText
dcterms.rights.dplaThis Item is protected by copyright and/or related rights (https://rightsstatements.org/vocab/InC/1.0/). You are free to use this Item in any way that is permitted by the copyright and related rights legislation that applies to your use. For other uses you need to obtain permission from the rights-holder(s).
thesis.degree.disciplineStatistics
thesis.degree.grantorColorado State University
thesis.degree.levelDoctoral
thesis.degree.nameDoctor of Philosophy (Ph.D.)

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