ONE WAY FANOVA USING PENALIZED SPLINES

Abstract

There are several methods available for smoothing scatter-plots. One interesting method involves using mixed model techniques that can be shown to be equivalent to the penalized splines method. In order to analyze certain functional data sets, we propose an extension of this mixed model approach that involves the smoothing of several scatter-plots simultaneously. More precisely, we show how one can estimate the mean profiles of functional data that have one grouping factor by fitting a single mixed model. The underlying mixed model will then be used to set up a hypotheses testing scheme for doing one way functional analysis of variance, FANOVA. In doing so, we will establish an interesting connection between the one way FANOVA problem and the problem of testing whether variance components from certain mixed models are zero. Finally we will propose a method for doing multiple comparisons in the functional setting, again using the underlying mixed model from the fitting criteria. The proposed methods are then demonstrated through an analysis of a typical functional data set.