Date of Award

5-2011

Document Type

Dissertation

Degree Name

Doctor of Philosophy (PhD)

Legacy Department

Mathematical Science

Advisor

Kulasekera, Karunarathna

Committee Member

Gallagher , Colin

Committee Member

Taylor , Robert

Committee Member

Padgett , William

Committee Member

Sun , Xiaoqian

Abstract

This dissertation aims to address two problems in nonparametric regression models. An estimation issue in generalized varying coefficient models and a hypothesis testing issue in nonparametric quantile regression models is discussed.
We propose a new estimation method for generalized varying coefficient models where the link function is specified up to some smoothness conditions. Consistency and asymptotic normality of the estimated varying coefficient functions are established. Simulation results and a real data application demonstrate the usefulness of the new method.
A new approach for testing the equality of nonparametric quantile regression functions is also presented. Based on marked empirical processes, we develop test statistics that possess $\sqrt n$ properties in contrast to all available procedures in the literature. Asymptotic distributions are given and the performance of the proposed tests is compared with existing methods in mean regression and quantile regression. Theoretical results show that our tests have superior local power properties over existing tests. Finite sample performance is analyzed through simulations under a variety of settings. A data analysis is given which highlights the usefulness of the proposed methodology.

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