The Annals of Statistics
- Ann. Statist.
- Volume 15, Number 3 (1987), 1131-1154.
Stochastic Estimation and Testing
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.
Ann. Statist., Volume 15, Number 3 (1987), 1131-1154.
First available in Project Euclid: 12 April 2007
Permanent link to this document
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
Primary: 62E20: Asymptotic distribution theory
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
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