The Annals of Statistics

Jackknifing Maximum Likelihood Estimates

James A. Reeds

Full-text: Open access

Abstract

This paper proves the apparently outstanding conjecture that the maximum likelihood estimate (m.l.e.) "behaves properly" when jackknifed. In particular, under the usual Cramer conditions (1) the jackknifed version of the consistent root of the m.l. equation has the same asymptotic distribution as the consistent root itself, and (2) the jackknife estimate of the variance of the asymptotic distribution of the consistent root is itself consistent. Further, if the hypotheses of Wald's consistency theorem for the m.l.e. are satisfied, then the above claims hold for the m.l.e. (as well as for the consistent root).

Article information

Source
Ann. Statist., Volume 6, Number 4 (1978), 727-739.

Dates
First available in Project Euclid: 12 April 2007

Permanent link to this document
https://projecteuclid.org/euclid.aos/1176344248

Digital Object Identifier
doi:10.1214/aos/1176344248

Mathematical Reviews number (MathSciNet)
MR483143

Zentralblatt MATH identifier
0436.62028

JSTOR
links.jstor.org

Subjects
Primary: 62F10: Point estimation
Secondary: 62E20: Asymptotic distribution theory 62F25: Tolerance and confidence regions

Keywords
Jackknife maximum likelihood estimate $M$-estimate asymptotic normality Banach space law of large numbers reversion of series Cramer conditions

Citation

Reeds, James A. Jackknifing Maximum Likelihood Estimates. Ann. Statist. 6 (1978), no. 4, 727--739. doi:10.1214/aos/1176344248. https://projecteuclid.org/euclid.aos/1176344248


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