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Empirical processes in action: A review. (English) Zbl 0757.62028

Summary: A review is given of recent applications of empirical process theory and methods to statistics with emphasis on empirical processes indexed by sets and functions. After a brief survey of empirical process theory, we review applications of this theory to estimation (censoring, truncation, biased sampling, regression and density function estimation, minimum distance methods), testing (classical goodness of fit and minimum distance tests, permutation and bootstrap tests, local alternatives and power), pattern recognition, clustering and classification, bootstrapping of empirical measures, and the delta method. One new theorem on the asymptotic behavior of empirical processes under local alternatives is presented.

MSC:

62G30 Order statistics; empirical distribution functions
62G07 Density estimation
62G10 Nonparametric hypothesis testing
62H30 Classification and discrimination; cluster analysis (statistical aspects)
62G20 Asymptotic properties of nonparametric inference
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