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Colloquium - 15 Feb 2000

Department of Statistics
Texas A&M University

ABSTRACT: The idea of dimension-reduction without loss of information can be quite helpful for guiding the construction of summary plots in regression without requiring a pre-specified model. Central subspaces are designed to capture all the information for the regression and to provide a population structure for dimension reduction. Recently, Cook and Li (1999) introduce the central mean subspace to capture the regression mean information. In this talk I first introduce a new central subspace called the central k-th moment subspace to capture information from the mean, variance and so on up to the k-th moment. New methods are studied for estimating these subspaces. Asymptotic distributions are developed, but in practice, a permanent test may be more useful. Connections with STR, pHd and SAVE are studied. Second, I consider inverse third moments to construct new methods to estimate directions in the central subspace. Examples illustrating the theory are presented. While mainly I focus on the regression context, these ideas, concepts and methods can be applied to many other problems, including classification and discriminant analysis.

Refreshments will be served in the Blocker Building, Room 447, at 3:30 p.m.

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