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ONE WAY FANOVA USING PENALIZED SPLINES

Author
Kormaksson, Matthias
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.
Date Issued
2007-06-12Subject
FANOVA; penalized splines; functional data; REML; scatter-plot smoothing; mixed model
Type
dissertation or thesis