Multiple Penalty Regression: Fitting and Extrapolating a Discrete Incomplete Multi-way Layout |
| |
Authors: | Rudolf Beran |
| |
Institution: | (1) Department of Statistics, University of California at Davis, Davis, CA 95616, USA |
| |
Abstract: | The d iscrete multi-way layout 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 paper 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 analysis of variance 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. |
| |
Keywords: | Nominal factor Ordinal factor Estimated risk Tensor-product penalty Multiparametric asymptotics Penalized least squares Bayes estimator |
本文献已被 SpringerLink 等数据库收录! |
|