Large and moderate deviations principles for recursive kernel estimators of a multivariate density and its partial derivatives

Abstract

In this paper we prove large and moderate deviations principles for the recursive kernel estimator of a probability density function and its partial derivatives. Unlike the density estimator, the derivatives estimators exhibit a quadratic behavior not only for the moderate deviations scale but also for the large deviations one. We provide results both for the pointwise and the uniform deviations.

26 pages

Cited by in corpus (2)

• Large and moderate deviation principles for recursive kernel density estimators defined by stochastic approximation method
• Large and moderate deviations principles for kernel estimators of the multivariate regression