L.S.T.A., University of Paris VI, 4, Place Jussieu, 75252 Paris cedex 05, France
Abstract:
We establish a large deviation limit theorem of Chernoff type for the L1-distance between the nonparametric kernel density estimator and the underlying density. The estimation is based on a sequence of independent and identically distributed random variables. The rate function is well identified, distribution-free and independent of the choice of the kernel.