Multiple Comparisons for Smoothed Fits to One- and Two-way Layouts
Rudolf Beran University of California, Davis
The multi-way layout is a fundamental data-type that has been treated diversely in ANOVA, in nonparametric regression, in image analysis, and elsewhere. ASP is a unified strategy for producing low risk shrinkage or smoothing fits to multi-way layouts without assuming that a submodel holds. The acronym, which stands for Adaptive Shrinkage on Penalty bases, reflects a link between ASP and penalized least squares. Features of potential interest in fitted means include peaks and troughs (for ordinal factors) and non-zero main effect or interaction terms (for nominal factors). We construct confidence balls about ASP fits to one- and two-way layouts, generate S-type multiple comparisons, and use these to assess the significance of features seen in ASP fits. The asymptotic theory is for layouts with one observation per cell and many cells.