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 variables. The limits are well-identified and depend upon the underlying kernel and density function. We derive then some implications of our results in the study of asymptotic efficiency of the goodness-of-fit test based on the maximal deviation of the kernel density estimator as well as the inaccuracy rate of this estimate