School Seminars and Colloquia

Regularized Regression: A Minimalist's Approach to Fitting and Extrapolating a Discrete Incomplete Multi-way Layout

Statistics Seminar

by Rudolf Beran

Institution: University of California, Davis
Date: Tue 4th March 2008
Time: 1:15 PM
Location: Room 213 Richard Berry Building The University of Melbourne

Abstract: The discrete multi-way layout with univariate responses is an abstract
data-type associated with regression, experimental designs, digital images or videos, spatial statistics, gene or protein chips, and more. The factors influencing response can be nominal or ordinal. The observed factor level combinations are finitely discrete and often incomplete or irregularly spaced. This talk develops low risk, biased estimators of the means at the observed factor level combinations; and extrapolates the
estimated means to larger discrete complete layouts. Candidate penalized least squares (PLS) estimators with multiple quadratic penalties express competing conjectures about each of the main effects and interactions in the ANOVA decomposition of the means. The candidate PLS estimator with smallest estimated quadratic risk attains, asymptotically, the smallest
risk over all candidate PLS estimators. In the theoretical analysis, the
dimension of the regression space tends to infinity. No assumptions are made about the unknown means or about replication. Extensions of the methodology to multi-way layouts with multivariate responses invoke a further possibility: reduction of the response dimension.

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