Abstract
This paper presents a method of nonparametric distribution estimation based on a sample level-crossing function, which leads to the construction of a level-crossing empirical distribution function (LCEDF). An efficiency function for this LCEDF relative to the classical empirical distribution function (e.d.f.) is derived. The LCEDF gives more efficient estimates than the e.d.f. in the tails of any underlying continuous distribution, for both small and large sample sizes. Simulation experiments, which apply the LCEDF to a smoothing technique for various distributions, confirm the theoretical results.
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