Estimation of the $k$th Derivative of a Distribution Function

Carl Maltz

doi:10.1214/aos/1176342670

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Home > Journals > Ann. Statist. > Volume 2 > Issue 2 > Article

March, 1974 Estimation of the $k$th Derivative of a Distribution Function

Carl Maltz

Ann. Statist. 2(2): 359-361 (March, 1974). DOI: 10.1214/aos/1176342670

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Abstract

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.

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Carl Maltz. "Estimation of the $k$th Derivative of a Distribution Function." Ann. Statist. 2 (2) 359 - 361, March, 1974. https://doi.org/10.1214/aos/1176342670

Information

Published: March, 1974

First available in Project Euclid: 12 April 2007

zbMATH: 0277.62033

MathSciNet: MR359160

Digital Object Identifier: 10.1214/aos/1176342670

Subjects:

Primary: 62G05

Secondary: 62F10

Keywords: asymptotic bias , asymptotic mean-square error , asymptotic variance , derivatives , difference quotients , distribution function , estimation