Inference for Parametric Empirical Processes

Parker, Thomas M.

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https://hdl.handle.net/2142/29733 Copy

Description

Title

Inference for Parametric Empirical Processes

Author(s)

Parker, Thomas M.

Issue Date

2012-02-06T20:13:34Z

Director of Research (if dissertation) or Advisor (if thesis)

Koenker, Roger W.

Committee Member(s)

• Bera, Anil K.
• Portnoy, Stephen L.
• Sowers, Richard B.

Department of Study

Economics

Discipline

Economics

Degree Granting Institution

University of Illinois at Urbana-Champaign

Degree Name

Ph.D.

Degree Level

Dissertation

Keyword(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.

Graduation Semester

2011-12

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http://hdl.handle.net/2142/29733

Copyright and License Information

Copyright 2011 Thomas M. Parker

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