The Annals of Statistics

Asymptotic Properties of Statistical Estimators in Stochastic Programming

Alexander Shapiro

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Abstract

The aim of this article is to investigate the asymptotic behaviour of estimators of the optimal value and optimal solutions of a stochastic program. These estimators are closely related to the $M$-estimators introduced by Huber (1964). The parameter set of feasible solutions is supposed to be defined by a number of equality and inequality constraints. It will be shown that in the presence of inequality constraints the estimators are not asymptotically normal in general. Maximum likelihood and robust regression methods will be discussed as examples.

Article information

Source
Ann. Statist., Volume 17, Number 2 (1989), 841-858.

Dates
First available in Project Euclid: 12 April 2007

Permanent link to this document
https://projecteuclid.org/euclid.aos/1176347146

Digital Object Identifier
doi:10.1214/aos/1176347146

Mathematical Reviews number (MathSciNet)
MR994271

Zentralblatt MATH identifier
0688.62025

JSTOR
links.jstor.org

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

Keywords
Stochastic programming $M$-estimators inequality constraints asymptotic normality cone approximation optimality conditions Lagrange multipliers

Citation

Shapiro, Alexander. Asymptotic Properties of Statistical Estimators in Stochastic Programming. Ann. Statist. 17 (1989), no. 2, 841--858. doi:10.1214/aos/1176347146. https://projecteuclid.org/euclid.aos/1176347146


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