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15
Asymptotics for Lassotype estimators
, 2000
"... this paper, we consider the asymptotic behaviour of regression estimators that minimize the residual sum of squares plus a penalty proportional to ..."
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Cited by 154 (3 self)
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this paper, we consider the asymptotic behaviour of regression estimators that minimize the residual sum of squares plus a penalty proportional to
Stochastic programming, in
 Handbooks in Operations Research and Management Science
, 1989
"... Abstract. Remarkable progress has been made in the development of algorithmic procedures and the availability of software for stochastic programming problems. However, some fundamental questions have remained unexplored. This paper identifies the more challenging open questions in the field of stoch ..."
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Cited by 25 (1 self)
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Abstract. Remarkable progress has been made in the development of algorithmic procedures and the availability of software for stochastic programming problems. However, some fundamental questions have remained unexplored. This paper identifies the more challenging open questions in the field of stochastic programming. Some are purely technical in nature, but many also go to the foundations of designing models for decision making under uncertainty.
EpiConvergence in Distribution and Stochastic EquiSemicontinuity
 C o rpusbased wo rk on discourse marke rs such as ‘ a n d ’ ,‘ i f’ , ‘ bu t ’ ,e
, 1997
"... : Epiconvergence in distribution is a useful tool in establishing limiting distributions of "argmin" estimators; however, it is not always easy to find the epilimit of a given sequence of objective functions. In this paper, we define the notion of stochastic equilowersemicontinuity of ..."
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Cited by 14 (2 self)
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: Epiconvergence in distribution is a useful tool in establishing limiting distributions of "argmin" estimators; however, it is not always easy to find the epilimit of a given sequence of objective functions. In this paper, we define the notion of stochastic equilowersemicontinuity of a sequence of random objective functions. It is shown that epiconvergence in distribution and finite dimensional convergence in distribution (to a given limit) of a sequence of random objective functions are equivalent under this condition. Key words and phrases: argmin estimators, convergence in distribution, epiconvergence, equisemicontinuity AMS 1991 subject classifications: Primary 62F12, 60F05; Secondary 62E20, 60F17. Running head: Stochastic equisemicontinuity 1 Introduction Many statistical estimators are defined as the minimizer (or maximizer) of some objective function; common examples include maximum likelihood estimation and Mestimation. Since any maximization problem can be reexp...
Estimating Density Functions: A Constrained Maximum Likelihood Approach
, 1998
"... We propose estimating density functions by means of a constrained optimization problem whose criterion function is the maximum likelihood function, and whose constraints model any (prior) information that might be available. The asymptotic justification for such an approach relies on the theory of e ..."
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Cited by 6 (0 self)
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We propose estimating density functions by means of a constrained optimization problem whose criterion function is the maximum likelihood function, and whose constraints model any (prior) information that might be available. The asymptotic justification for such an approach relies on the theory of epiconvergence. A simple numerical example is used to signal the potential of such an approach.
Stochastic Integer Programming: Limit Theorems and Confidence Intervals
"... informs doi 10.1287/moor.1060.0222 ..."
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Differentiable Selections of SetValued Mappings With Application in Stochastic Programming
"... We consider setvalued mappings defined on a linear normed space with convex closed images in R^n. Our aim is to construct selections which are (Hadamard) directionally differentiable using some approximation of the multifunction. The constructions suggested assume existence of a cone approximation ..."
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Cited by 2 (1 self)
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We consider setvalued mappings defined on a linear normed space with convex closed images in R^n. Our aim is to construct selections which are (Hadamard) directionally differentiable using some approximation of the multifunction. The constructions suggested assume existence of a cone approximation given by a certain "derivative" of the mapping. The first one makes use of the properties of Steiner points. The notion of Steiner center is generalized for a class of unbounded sets, which include the polyhedral sets. The second construction defines a continuous selection through a given point of the graph of the multifunction and being Hadamard directionally differentiable at that point with derivatives belonging to the corresponding "derivative" of the multifunction. Both constructions lead to a directionally differentiable Castaing representation of measurable multifunctions with the required differentiability properties. The results are applied to obtain statements about the asymptotic behaviour of measurable selections of random sets via the deltaapproach. Particularly, random sets of this kind build the solutions of twostage stochastic programs.
Asymptotic theory for Mestimators over a convex kernel. Econometric Theory
 RIAO 2000 Joseph Mariani and Donna Harman, CoChairs of the RIAO 2000 Scientific
, 1998
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MATRIX COMPLETION MODELS WITH FIXED BASIS COEFFICIENTS AND RANK REGULARIZED PROBLEMS WITH HARD CONSTRAINTS
, 2013
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Regular Castaing Representations of Multifunctions with Applications to Stochastic Programming
, 1998
"... We consider setvalued mappings de ned on a topological space with convex closed images in IR n. The measurability ofamultifunction is characterized by the existence of a Castaing representation for it: a countable set of measurable selections that pointwise ll up the graph of the multifunction. Our ..."
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We consider setvalued mappings de ned on a topological space with convex closed images in IR n. The measurability ofamultifunction is characterized by the existence of a Castaing representation for it: a countable set of measurable selections that pointwise ll up the graph of the multifunction. Our aim is to construct a Castaing representation which inherits the regularity properties of the multifunction. The construction uses Steiner points. A notion of a generalized Steiner point is introduced. A Castaing representation called regular is de ned by using generalized Steiner selections. All selections are measurable, continuous, resp. Holdercontinuous, or directionally di erentiable, if the multifunction has the corresponding properties. The results are applied to various multifunctions arising in stochastic programming. In particular, statements about the asymptotic behavior of measurable selections of solution sets via the deltamethod are obtained. Keywords: Steiner center, selections, Castaing representation, stochastic programs, random sets, deltatheorems