ASP fits to multi-way layouts |
| |
Authors: | Rodolf Beran |
| |
Institution: | (1) Department of Statistics, University of California, Davis, 95616 Davis, CA, USA |
| |
Abstract: | The balanced complete multi-way layout with ordinal or nominal factors is a fundamental data-type that arises in medical imaging,
agricultural field trials, DNA microassays, and other settings where analysis of variance (ANOVA) is an established tool.
ASP algorithms weigh competing biased fits in order to reduce risk through variance-bias tradeoff. The acronym ASP stands
for Adaptive Shrinkage of Penalty bases. Motivating ASP is a penalized least squares criterion that associates a separate
quadratic penalty term with each main effect and each interaction in the general ANOVA decomposition of means. The penalty
terms express plausible conjecture about the mean function, respecting the difference between ordinal and nominal factors.
Multiparametric asymptotics under a probability model and experiments on data elucidate how ASP dominates least squares, sometimes
very substantially. ASP estimators for nominal factors recover Stein's superior shrinkage estimators for one- and two-way
layouts. ASP estimators for ordinal factors bring out the merits of smoothed fits to multi-way layouts, a topic broached algorithmically
in work by Tukey.
This research was supported in part by National Science Foundation Grants DMS 0300806 and 0404547. |
| |
Keywords: | Nominal factors ordinal factors estimated risk penalized least squares annihilator matrix balanced complete layout multiparametric asymptotics |
本文献已被 SpringerLink 等数据库收录! |
|