JSM 2005 - Toronto

Abstract #303096

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Legend: = Applied Session, = Theme Session, = Presenter
Activity Number: 364
Type: Contributed
Date/Time: Wednesday, August 10, 2005 : 8:30 AM to 10:20 AM
Sponsor: General Methodology
Abstract - #303096
Title: Improved Estimation of Dissimilarities by Presmoothing Functional Data
Author(s): David B. Hitchcock*+ and George Casella and James G. Booth
Companies: University of South Carolina and University of Florida and Cornell University
Address: 116 Great North Road, Columbia, SC, 29223,
Keywords: Distance methods ; Dissimilarity measures ; Cluster analysis ; Multidimensional scaling ; Stein estimation ; Shrinkage estimation
Abstract:

We examine the effect of presmoothing functional data on estimating the dissimilarities among objects in a dataset, with applications to cluster analysis and other distance methods such as multidimensional scaling and statistical matching. We prove a shrinkage method of smoothing results in a better estimator of the dissimilarities among a set of noisy curves. For a model having independent noise structure, the smoothed-data dissimilarity estimator dominates the observed-data estimator. For a dependent-error model---often applicable when the functional data are measured nearly continuously over some domain---an asymptotic domination result is given for the smoothed-data estimator. The shrinkage estimator presented here combines Stein estimation and basis function-based linear smoothers in a novel manner. Statisticians increasingly analyze sizable sets of functional data. The results in this paper contribute to the theory of the effect of presmoothing on functional data analysis.

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Revised March 2005