Large and moderate deviations principles for recursive kernel estimators   of a multivariate density and its partial derivatives
  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. 
Abdelkader Mokkadem, Mariane Pelletier, Baba Thiam