Journal ArticleDOI
Asymptotic analysis of stochastic programs
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The approach is based on an extended delta method and appears to be particularly suitable for deriving asymptotics of the optimal value of stochastic programs.Abstract:
In this paper we discuss a general approach to studying asymptotic properties of statistical estimators in stochastic programming. The approach is based on an extended delta method and appears to be particularly suitable for deriving asymptotics of the optimal value of stochastic programs. Asymptotic analysis of the optimal value will be presented in detail. Asymptotic properties of the corresponding optimal solutions are briefly discussed.read more
Citations
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Book
Lectures on Stochastic Programming: Modeling and Theory
TL;DR: The authors dedicate this book to Julia, Benjamin, Daniel, Natan and Yael; to Tsonka, Konstatin and Marek; and to the Memory of Feliks, Maria, and Dentcho.
Journal ArticleDOI
The Sample Average Approximation Method for Stochastic Discrete Optimization
TL;DR: A Monte Carlo simulation--based approach to stochastic discrete optimization problems, where a random sample is generated and the expected value function is approximated by the corresponding sample average function.
Book ChapterDOI
Monte Carlo Sampling Methods
TL;DR: In this article, Monte Carlo sampling methods for solving large scale stochastic programming problems are discussed, where a random sample is generated outside of an optimization procedure, and then the constructed, so-called sample average approximation (SAA), problem is solved by an appropriate deterministic algorithm.
References
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Book
Convergence of Probability Measures
TL;DR: Weak Convergence in Metric Spaces as discussed by the authors is one of the most common modes of convergence in metric spaces, and it can be seen as a form of weak convergence in metric space.
Book
Linear statistical inference and its applications
TL;DR: Algebra of Vectors and Matrices, Probability Theory, Tools and Techniques, and Continuous Probability Models.
Journal ArticleDOI
Robust Estimation of a Location Parameter
TL;DR: In this article, a new approach toward a theory of robust estimation is presented, which treats in detail the asymptotic theory of estimating a location parameter for contaminated normal distributions, and exhibits estimators that are asyptotically most robust (in a sense to be specified) among all translation invariant estimators.
The behavior of maximum likelihood estimates under nonstandard conditions
TL;DR: In this paper, the authors prove consistency and asymptotic normality of maximum likelihood estimators under weaker conditions than usual, such that the true distribution underlying the observations belongs to the parametric family defining the estimator, and the regularity conditions do not involve the second and higher derivatives of the likelihood function.