Author

Erol Ozkan

ORCID Identifier(s)

0000-0002-0924-252X

Graduation Semester and Year

2021

Language

English

Document Type

Dissertation

Degree Name

Doctor of Philosophy in Mathematics

Department

Mathematics

First Advisor

SHAN SUN-MITCHELL

Abstract

In this study, we propose a new regression function estimator when the observa- tion is contaminated in the convolution model with error in independent variable. We want to examine the e ect of the error variables when the data is right censored. The tail behavior of the characteristic function of the error distribution is used to describe the optimum local and global rates of convergence of these kernel estimators. We show that depending on the error is either ordinary smooth or super smooth, there are two sorts of convergence rates in adjusted mean square error for the regression function estimator. It is observed that the rate of convergence is slower in super smooth model for both locally and globally, whereas it is faster in ordinary smooth model. Furthermore, it is examined that in nonparametric regression function estimation, the choice of the kernel K has very little impact on optimality (in the MSE sense), but the bandwidth h has signi cant impact. Simulation are drawn for di erent sample sizes in two di erent examples with 100 replications for each of the samples.

Keywords

Kernel regression

Disciplines

Mathematics | Physical Sciences and Mathematics

Comments

Degree granted by The University of Texas at Arlington

Included in

Mathematics Commons

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