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
  • 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.