Asymptotic Properties of Statistical Estimators in Stochastic Programming
Shapiro, Alexander
Ann. Statist., Tome 17 (1989) no. 1, p. 841-858 / Harvested from Project Euclid
Text on Project Euclid
PDF
Alt PDF
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.
Publié le : 1989-06-14
Classification:  Stochastic programming,  $M$-estimators,  inequality constraints,  asymptotic normality,  cone approximation,  optimality conditions,  Lagrange multipliers,  62F12,  90C15 
@article{1176347146,
     author = {Shapiro, Alexander},
     title = {Asymptotic Properties of Statistical Estimators in Stochastic Programming},
     journal = {Ann. Statist.},
     volume = {17},
     number = {1},
     year = {1989},
     pages = { 841-858},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1176347146}
}

Shapiro, Alexander. Asymptotic Properties of Statistical Estimators in Stochastic Programming. Ann. Statist., Tome 17 (1989) no. 1, pp.  841-858. http://gdmltest.u-ga.fr/item/1176347146/