Density estimation stochastic approximation algorithm large and moderate deviations principles
Institute of Mathematics and Informatics Bulgarian Academy of Sciences
Serdica Mathematical Journal, Vol. 39, No 1, (2013), 53p-82p
In this paper we prove large and moderate deviations principles for the recursive kernel estimators of a probability density function defined by the stochastic approximation algorithm introduced by Mokkadem et al.(. The stochastic approximation method for the estimation of a probability density. J. Statist. Plann. Inference 139 (2009), 2459–2478). We
show that the estimator constructed using the stepsize which minimize the variance of the class of the recursive estimators defined in  gives the same pointwise LDP and MDP as the Rosenblatt kernel estimator. We provide
results both for the pointwise and the uniform deviations.