Pointwise Sharp Moderate Deviations for a Kernel Density Estimator

Abstract

Let fn be the non-parametric kernel density estimator based on a kernel function K and a sequence of independent and identically distributed random vectors taking values in Rd. With some mild conditions, we establish sharp moderate deviations for the kernel density estimator. This means that we provide an equivalent for the tail probabilities of this estimator.

Keywords

• Cramér moderate deviations
• kernel density estimator
• kernel function