ASYMPTOTIC NORMALITY OF THE DECONVOLUTION KERNEL DENSITY ESTIMATORS BASED ON INDEPENDENT AS WELL AS STRONG MIXING RIGHT CENSORED DATA

Author

Wenqing Zhu

Graduation Semester and Year

2020

Language

English

Document Type

Dissertation

Degree Name

Doctor of Philosophy in Mathematics

Department

Mathematics

First Advisor

Shan Sun-Mitchell

Abstract

We consider estimation of a density when observed lifetime from the convolution model contaminated by additive measurement errors. A kernel type deconvolution density estimator of the unknown distribution based on right censored data is proposed by using the Inverse-Probability-of-Censoring Weighted Average. Further, we discuss the asymptotic normality of the deconvolution kernel density estimators for independent and strong mixing vectors when the error distribution function is either ordinary smooth or supersmooth. Our method is applied to the study conducted by UTSW medical center. The research team at UTSW collected the data of women who underwent cystoscopy fulguration for recurrent urinary tract infection (UTI) from 2004-2016. Using the estimators and the asymptotic distributions of the estimators, we estimate the survival probability of the time from infection to recurrent UTI.

Keywords

Deconvolution, Asymptotic normality, Censored data

Disciplines

Mathematics | Physical Sciences and Mathematics

License

This work is licensed under a Creative Commons Attribution-NonCommercial-Share Alike 4.0 International License.

Comments

Degree granted by The University of Texas at Arlington

Recommended Citation

Zhu, Wenqing, "ASYMPTOTIC NORMALITY OF THE DECONVOLUTION KERNEL DENSITY ESTIMATORS BASED ON INDEPENDENT AS WELL AS STRONG MIXING RIGHT CENSORED DATA" (2020). Mathematics Dissertations. 208.
https://mavmatrix.uta.edu/math_dissertations/208