The Annals of Statistics

Stochastic Estimation and Testing

R. Beran and P. W. Millar

Full-text: Open access

Abstract

Stochastic procedures are randomized tests, estimates and confidence sets with two properties: (i) They are functions of an original sample and one or more artificially constructed auxiliary samples. (ii) They become nearly nonrandomized when the auxiliary samples increase in size. The stochastic procedures of this paper, which arise as approximations to numerically intractable procedures, involve iterated bootstrap techniques and random sampling schemes over abstract populations. A general methodology is applied to the asymptotic study of stochastic minimum distance tests, stochastic maximum likelihood estimates, stochastic confidence bands and several other stochastic procedures.

Article information

Source
Ann. Statist., Volume 15, Number 3 (1987), 1131-1154.

Dates
First available in Project Euclid: 12 April 2007

Permanent link to this document
https://projecteuclid.org/euclid.aos/1176350497

Digital Object Identifier
doi:10.1214/aos/1176350497

Mathematical Reviews number (MathSciNet)
MR902250

Zentralblatt MATH identifier
0644.62028

JSTOR
links.jstor.org

Subjects
Primary: 62E20: Asymptotic distribution theory

Keywords
Confidence set critical value bootstrap Monte Carlo minimum distance estimate goodness-of-fit test likelihood ratio test maximum likelihood estimate stochastic search confidence band for a measure empirical measure

Citation

Beran, R.; Millar, P. W. Stochastic Estimation and Testing. Ann. Statist. 15 (1987), no. 3, 1131--1154. doi:10.1214/aos/1176350497. https://projecteuclid.org/euclid.aos/1176350497


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