[IEEE Trans. on Information Theory, May. 1985, pp. 677-687]
Nonparametric Estimation via Empirical Risk Minimization
Gábor Lugosi and Kenneth Zeger
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.