Mathematics Department
Illinois State University
Normal, Illinois

Strong Consistency of Kernel Estimators of Cumulative Distribution Functions

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

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