Large Deviations Limit Theorems for the Kernel Density Estimator

Abstract

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