Large and moderate deviation principles for nonparametric recursive kernel distribution estimators defined by stochastic approximation method

Abstract

In this paper we prove large and moderate deviations principles for the recursive kernel estimators of a distribution function defined by the stochastic approximation algorithm. We show that the estimator constructed using the stepsize which minimize the Mean Integrated Squared Error (MISE) of the class of the recursive estimators defined by Mokkadem et al. gives the same pointwise large deviations principle (LDP) and moderate deviations principle (MDP) as the Nadaraya kernel distribution estimator.