Estimation of the $k$th Derivative of a Distribution Function
分布函数的 k 阶导数估计
Estimation of the $k$th derivative of a df by means of the $k$th-order difference quotients of the empiric df is investigated. In particular, consistency conditions are given, the asymptotic bias, variance, and mean-squared error of the estimator are computed, and means of minimizing the latter are discussed.