A Necessary and Sufficient Condition for the Asymptotic Normality of the Quantile Estimator in the Deconvolution Problem

Author

Jeremy R. Valdez

ORCID Identifier(s)

0000-0001-8232-214X

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 this study, we examine the estimation of a quantile function when we have n observations coming from the convolution model contaminated by additive measurement errors. Under certain assumptions, a kernel type deconvolution quantile estimator of the unknown quantile function is proposed. Moreover, we discuss the necessary and sufficient condition on the bandwidth in order to investigate the limiting distribution of the deconvolution kernel quantile estimator when the error terms follow either an ordinary smooth or super smooth distribution. A bootstrap approach is used to select the optimal bandwidth to construct approximate distribution free confidence bands for the quantile function Q(p). A Monte Carlo simulation study is conducted for different sample sizes to assess the performance of our estimator using the bootstrap procedure based off of 1000 replications for each of the samples. Lastly, an application using the deconvolution kernel quantile estimator is examined on earthquake data.

Keywords

Asymptotic normality, Deconvolution, Kernel estimation, Bandwidth

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

Valdez, Jeremy R., "A Necessary and Sufficient Condition for the Asymptotic Normality of the Quantile Estimator in the Deconvolution Problem" (2022). Mathematics Dissertations. 203.
https://mavmatrix.uta.edu/math_dissertations/203