Open Access
Translator Disclaimer
May, 1980 A Note on Differentials and the CLT and LIL for Statistical Functions, with Application to $M$-Estimates
Dennis D. Boos, R. J. Serfling
Ann. Statist. 8(3): 618-624 (May, 1980). DOI: 10.1214/aos/1176345012

Abstract

A parameter expressed as a functional $T(F)$ of a distribution function (df) $F$ may be estimated by the "statistical function" $T(F_n)$ based on the sample df $F_n$. For analysis of the estimation error $T(F_n) - T(F)$, we adapt the differential approach of von Mises (1947) to exploit stochastic properties of the Kolmogorov-Smirnov distance $\sup_x|F_n(x) - F(x)|$. This leads directly to the central limit theorem (CLT) and law of the iterated logarithm (LIL) for $T(F_n) - T(F)$. The adaptation also incorporates innovations designed to broaden the scope of statistical application of the concept of differential. Application to a wide class of robust-type $M$-estimates is carried out.

Citation

Download Citation

Dennis D. Boos. R. J. Serfling. "A Note on Differentials and the CLT and LIL for Statistical Functions, with Application to $M$-Estimates." Ann. Statist. 8 (3) 618 - 624, May, 1980. https://doi.org/10.1214/aos/1176345012

Information

Published: May, 1980
First available in Project Euclid: 12 April 2007

zbMATH: 0434.62022
MathSciNet: MR568724
Digital Object Identifier: 10.1214/aos/1176345012

Subjects:
Primary: 62E20
Secondary: 62G35

Rights: Copyright © 1980 Institute of Mathematical Statistics

JOURNAL ARTICLE
7 PAGES


SHARE
Vol.8 • No. 3 • May, 1980
Back to Top