Robust functional estimation using the median and spherical principal components

We present robust estimators for the mean and the principal components of a stochastic process in . 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...

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Bibliographic Details
Published in:Biometrika 2008-09, Vol.95 (3), p.587-600
Main Author: Gervini, Daniel
Format: Article
Language:English
Subjects:
Applications
Biology, psychology, social sciences
Breakdown point
Consistent estimators
Covariance
Data lines
Eigenfunctions
Eigenvalues
Error rates
Estimators
Exact sciences and technology
General topics
Influence function
Mathematics
Multivariate analysis
Nonparametric regression
Outlier detection
Probability and statistics
Probability theory and stochastic processes
Regression analysis
Sample mean
Sciences and techniques of general use
Simulation
Statistical median
Statistics
Stochastic models
Stochastic process
Stochastic processes
Studies
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Description
Summary:We present robust estimators for the mean and the principal components of a stochastic process in . 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.
ISSN:0006-3444
1464-3510
DOI:10.1093/biomet/asn031