The Annals of Statistics

Asymptotic Behavior of Statistical Estimators and of Optimal Solutions of Stochastic Optimization Problems

Jitka Dupacova and Roger Wets

Full-text: Open access

Abstract

We study the asymptotic behavior of the statistical estimators that maximize a not necessarily differentiable criterion function, possibly subject to side constraints (equalities and inequalities). The consistency results generalize those of Wald and Huber. Conditions are also given under which one is still able to obtain asymptotic normality. The analysis brings to the fore the relationship between the problem of finding statistical estimators and that of finding the optimal solutions of stochastic optimization problems with partial information. The last section is devoted to the properties of the saddle points of the associated Lagrangians.

Article information

Source
Ann. Statist., Volume 16, Number 4 (1988), 1517-1549.

Dates
First available in Project Euclid: 12 April 2007

Permanent link to this document
https://projecteuclid.org/euclid.aos/1176351052

Digital Object Identifier
doi:10.1214/aos/1176351052

Mathematical Reviews number (MathSciNet)
MR964937

Zentralblatt MATH identifier
0667.62018

JSTOR
links.jstor.org

Subjects
Primary: 62F12: Asymptotic properties of estimators
Secondary: 62A10 90C15: Stochastic programming

Keywords
Statistical estimators consistency stochastic programming epi-convergence asymptotically normal subdifferentiability

Citation

Dupacova, Jitka; Wets, Roger. Asymptotic Behavior of Statistical Estimators and of Optimal Solutions of Stochastic Optimization Problems. Ann. Statist. 16 (1988), no. 4, 1517--1549. doi:10.1214/aos/1176351052. https://projecteuclid.org/euclid.aos/1176351052


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