LARGE DEVIATIONS LIMIT-THEOREMS FOR THE KERNEL DENSITY ESTIMATOR

We establish pointwise and uniform large deviations limit theorems of Chernoff-type for the non-parametric kernel density estimator based on a sequence of independent and identically distributed random variable s. The limits are well-identified and depend upon the underlying kerne l and density function. We derive then some implications of our result s in the study of asymptotic efficiency of the goodness-of-fit test ba sed on the maximal deviation of the kernel density estimator as well a s the inaccuracy rate of this estimate.