An Alternative Estimator of the Empirical Cumulative Distribution Function Based on Order Statistics
摘要
We introduce an alternative estimator for the cumulative distribution function (CDF) that, unlike the standard empirical CDF, is constructed using the order statistics of a given independent and identically distributed sample rather than the raw sample itself. In this paper, we take an initial step toward studying the asymptotic properties of this estimator and provide numerical evidence that it achieves a lower mean squared error compared to the traditional empirical CDF.