Asymptotic Properties of the Deconvolution Kernel Density Estimate based on 2-Dependent Error Structure with Applications to Remaining Useful Life Problems in Reliability Theory

Author

Geoffrey H. Schuette

Graduation Semester and Year

2018

Language

English

Document Type

Dissertation

Degree Name

Doctor of Philosophy in Mathematics

Department

Mathematics

First Advisor

Shan Sun-Mitchell

Abstract

This thesis is motivated from an engineering question, which led us to the deconvolution problem with a dependent error structure. We establish a deconvolution kernel density estimator by adapting the methods of kernel density estimates and Fourier Transforms. In this approach, the contaminated data with additive random errors are assumed dependent and satisfying smooth or super smooth conditions. Under both smooth and supper smooth conditions, we derived: 1. optimal rates of convergence in terms of mean integrated squared error for deconvolution kernel density estimator; 2. the limiting distribution of the estimator.

Keywords

Deconvolution, Kernel Density Estimation

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

Schuette, Geoffrey H., "Asymptotic Properties of the Deconvolution Kernel Density Estimate based on 2-Dependent Error Structure with Applications to Remaining Useful Life Problems in Reliability Theory" (2018). Mathematics Dissertations. 245.
https://mavmatrix.uta.edu/math_dissertations/245