Annals of Statistics

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

Carl Maltz

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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.

Article information

Source
Ann. Statist., Volume 2, Number 2 (1974), 359-361.

Dates
First available in Project Euclid: 12 April 2007

Permanent link to this document
https://projecteuclid.org/euclid.aos/1176342670

Digital Object Identifier
doi:10.1214/aos/1176342670

Mathematical Reviews number (MathSciNet)
MR359160

Zentralblatt MATH identifier
0277.62033

JSTOR
links.jstor.org

Subjects
Primary: 62G05: Estimation
Secondary: 62F10: Point estimation

Keywords
Estimation derivatives distribution function difference quotients asymptotic variance asymptotic mean-square error asymptotic bias

Citation

Maltz, Carl. Estimation of the $k$th Derivative of a Distribution Function. Ann. Statist. 2 (1974), no. 2, 359--361. doi:10.1214/aos/1176342670. https://projecteuclid.org/euclid.aos/1176342670


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