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
License
This work is licensed under a Creative Commons Attribution-NonCommercial-Share Alike 4.0 International License.
Recommended Citation
Khakurel, Hrishabh, "Performance of Density Estimators in Additive Measurement Error Models Based on Right Censored Data" (2022). Mathematics Dissertations. 211.
https://mavmatrix.uta.edu/math_dissertations/211
Comments
Degree granted by The University of Texas at Arlington