The Law of the Iterated Logarithm for <i>L</i>_p-Norms of Kernel Estimators of Cumulative Distribution Functions

Abstract

In this paper, we consider the strong convergence of Lp-norms (p≥1) of a kernel estimator of a cumulative distribution function (CDF). Under some mild conditions, the law of the iterated logarithm (LIL) for the Lp-norms of empirical processes is extended to the kernel estimator of the CDF.

Keywords

• Lp-norm
• LIL
• kernel estimator
• empirical CDF