Nonparametric estimation via empirical risk minimization

Authors:
G. Lugosi;K. Zeger
Affiliations:
Dept. of Math. & Comput. Sci., Tech. Univ. Budapest;-
Venue:
IEEE Transactions on Information Theory
Year:
1995

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Abstract

A general notion of universal consistency of nonparametric estimators is introduced that applies to regression estimation, conditional median estimation, curve fitting, pattern recognition, and learning concepts. General methods for proving consistency of estimators based on minimizing the empirical error are shown. In particular, distribution-free almost sure consistency of neural network estimates and generalized linear estimators is established