ORCID Identifier(s)

0000-0001-5328-8034

Graduation Semester and Year

2022

Language

English

Document Type

Dissertation

Degree Name

Doctor of Philosophy in Mathematics

Department

Mathematics

First Advisor

Shan Sun-Mitchell

Abstract

In the deconvolution problem for right censored data, one is interested in estimating the density of a contaminated variable X when X satisfies Z= X+ E, where E is a measurement error with a known distribution, and the observable variable Z is right-censored. Zhu, Sun, Khakurel, and Wang (2021) applied the Inverse Probability of Censoring Weighted Average method and derived the estimators of the unknown density of X. In this study, we evaluate the performance of the density estimators both in theory and in simulation. We derive the theoretical upper bounds for Mean Squared Error (MSE) of the estimator and its derivatives, accounting for the tail behavior of the error distribution. Our simulation studies focus on: (a) the problem of estimating the unknown censoring distribution, (b) methods of selecting the optimal bandwidth, and (c) the effects of the kernel and error distributions on the density estimators. Our simulations show that the estimators perform reasonably well when sample sizes are relatively large.

Keywords

Density estimation, Kernel density estimation, Right censored, Additive measurement errors

Disciplines

Mathematics | Physical Sciences and Mathematics

Comments

Degree granted by The University of Texas at Arlington

Included in

Mathematics Commons

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