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Biometrika 2008 95(3):587-600; doi:10.1093/biomet/asn031
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© 2008 Biometrika Trust

Articles

Robust functional estimation using the median and spherical principal components

Daniel Gervini

Department of Mathematical Sciences, University of Wisconsin, P.O. Box 413, Milwaukee, Wisconsin 53201, U.S.A. gervini{at}uwm.edu

Received for publication 1 May 2007. Revision received 1 February 2008.
  Abstract

We present robust estimators for the mean and the principal components of a stochastic process in Formula . Robustness and asymptotic properties of the estimators are studied theoretically, by simulation and by example. It is shown that the proposed estimators are generally more robust to outliers than the commonly used sample mean and principal components, although their properties depend on the spacings of the eigenvalues of the covariance function.

Key Words: Breakdown point • Influence function • Nonparametric regression • Outlier detection • Stochastic process


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