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Inference for Parametric Empirical Processes

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Title: Inference for Parametric Empirical Processes
Author(s): Parker, Thomas M.
Advisor(s): Koenker, Roger
Contributor(s): Bera, Anil; Portnoy, Stephen; Sowers, Richard
Department / Program: Economics
Discipline: Economics
Degree Granting Institution: University of Illinois at Urbana-Champaign
Degree: Ph.D.
Genre: Doctoral
Subject(s): Empirical processes Goodness of fit testing Empirical characteristic function Stochastic dominance Gaussian field approximations
Abstract: Parametric empirical processes, empirical processes that incorporate parametric modeling components into their definition, play a natural role in many inferential settings. In this dissertation we illustrate their application, highlighting methods for inference that rely on supremum-norm test statistics. Chapter 1 illustrates the use of supremum-norm statistics for inference in simple parametric modeling situations. The estimation of parameters alters the distribution of commonly-used test statistics, but methods are explored that accommodate these differences using approximations based on features of the parametric model. Chapter 2 extends this methodology to tests based on a group of related processes, kernel- transformed empirical processes. It is shown that a martingale transform coupled with the kernel trans- formation results in processes that have simple limiting distributions. This makes them attractive for inference because their tractability facilitates straightforward calculation of approximate critical values in a variety of cases. Chapter 3 extends this methodology in a different direction, to two-sample tests of stochastic dominance. Tests for any order of dominance are considered, and the distribution of test statistics is shown to be related to the family of iteratively integrated Brownian bridges. A Rice series approximation, used to find boundary crossing probabilities for smooth Gaussian processes, is proposed as an inferential method. Tests that use residuals from conditional models are also considered and it is shown that their distribution is nonstandard due to the way in which the residuals are incorporated into tests. It is shown how approximate critical values can be altered to reflect this estimation effect.
Issue Date: 2012-02-06
Genre: thesis
Rights Information: Copyright 2011 Thomas M. Parker
Date Available in IDEALS: 2012-02-06
Date Deposited: 2011-12

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