Improved estimation of dissimilarities by presmoothing functional data
成果类型：
Article
署名作者：
Hitchcock, DB; Casella, G; Booth, JG
署名单位：
University of South Carolina System; University of South Carolina Columbia; State University System of Florida; University of Florida; Cornell University
刊物名称：
JOURNAL OF THE AMERICAN STATISTICAL ASSOCIATION
ISSN/ISSBN：
0162-1459
DOI：
10.1198/016214505000000673
发表日期：
2006
页码：
211-222
关键词：
摘要：
We examine the effect of presmoothing functional data oil 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 that a shrinkage method of smoothing results in a better estimator of the dissimilarities among a set of noisy curves. For a model with 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. A simulation study indicates the magnitude of improvement provided by the shrinkage estimator and examines its behavior for heavy-tailed noise structure. 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. and the results in this article are a useful contribution to the theory of the effect of presmoothing oil functional data analysis.