Dimension Reduction for Non-elliptically Distributed Predictors
Open Access
Author:
Dong, Yuexiao
Graduate Program:
Statistics
Degree:
Doctor of Philosophy
Document Type:
Dissertation
Date of Defense:
December 18, 2008
Committee Members:
Bing Li, Committee Chair/Co-Chair Michael G. Akritas, Committee Member Runze Li, Committee Member Dennis K. J. Lin, Committee Member
Keywords:
central space dimension reduction solution space non-ellipticity
Abstract:
Many classical dimension reduction methods require the predictors to have elliptical distributions, or at least to satisfy a linearity
condition. In this dissertation we reformulate the commonly used dimension reduction methods to circumvent the requirement of such strong assumptions, while at the same time preserve the desirable properties of the classical methods, such as consistency and asymptotic normality. The notion of "central solution space" is introduced first. We then use it to modify essentially all inverse conditional moment based methods under a general framework. Imposing elliptical distributions or even stronger assumptions on predictors is often considered as
the necessary tradeoff for overcoming the "curse of dimensionality", but the development of this dissertation shows this need not be the case.
