Estimation of the $k$th Derivative of a Distribution Function
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.
Permanent link to this document: http://projecteuclid.org/euclid.aos/1176342670
Digital Object Identifier: doi:10.1214/aos/1176342670
Mathematical Reviews number (MathSciNet): MR359160
Zentralblatt MATH identifier: 0277.62033