Author ORCID Identifier

https://orcid.org/0000-0001-7888-1387

Year of Publication

2017

Degree Name

Doctor of Philosophy (PhD)

Document Type

Doctoral Dissertation

College

Arts and Sciences

Department

Statistics

First Advisor

Dr. Richard Charnigo

Abstract

Firstly, we reviewed some popular nonparameteric regression methods during the past several decades. Then we extended the compound estimation (Charnigo and Srinivasan [2011]) to adapt random design points and heteroskedasticity and proposed a modified Cp criteria for tuning parameter selection. Moreover, we developed a DCp criteria for tuning paramter selection problem in general nonparametric derivative estimation. This extends GCp criteria in Charnigo, Hall and Srinivasan [2011] with random design points and heteroskedasticity. Next, we proposed a change point detection method via compound estimation for both fixed design and random design case, the adaptation of heteroskedasticity was considered for the method. Finally, we applied our change point detection method to a glucose level data set and identified the meal consumption time for five patients.

Digital Object Identifier (DOI)

https://doi.org/10.13023/ETD.2017.312

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