Results 1  10
of
18
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 ..."
Abstract

Cited by 254 (3 self)
 Add to MetaCart
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 ..."
Abstract

Cited by 34 (1 self)
 Add to MetaCart
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 ..."
Abstract

Cited by 21 (4 self)
 Add to MetaCart
: 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 ..."
Abstract

Cited by 8 (0 self)
 Add to MetaCart
(Show Context)
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.
A RankCorrected Procedure for Matrix Completion with Fixed Basis Coefficients
, 2012
"... In this paper, we address lowrank matrix completion problems with fixed basis coefficients, which include the lowrank correlation matrix completion in various fields such as the financial market and the lowrank density matrix completion from the quantum state tomography. For this class of problem ..."
Abstract

Cited by 6 (2 self)
 Add to MetaCart
In this paper, we address lowrank matrix completion problems with fixed basis coefficients, which include the lowrank correlation matrix completion in various fields such as the financial market and the lowrank density matrix completion from the quantum state tomography. For this class of problems, the efficiency of the common nuclear norm penalized estimator for recovery may be challenged. Here, with a reasonable initial estimator, we propose a rankcorrected procedure to generate an estimator of high accuracy and low rank. For this new estimator, we establish a nonasymptotic recovery error bound and analyze the impact of adding the rankcorrection term on improving the recoverability. We also provide necessary and sufficient conditions for rank consistency in the sense of Bach [3], in which the concept of constraint nondegeneracy in matrix optimization plays an important role. As a byproduct, our results provide a theoretical foundation for the majorized penalty method of Gao and Sun [25] and Gao [24] for structured lowrank matrix optimization problems.
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 ..."
Abstract

Cited by 2 (1 self)
 Add to MetaCart
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
"... ..."
On the asymptotic distribution of the Chebyshev estimator in linear regression
, 2010
"... The Chebyshev or L ∞ estimator minimizes the maximum absolute residual and is useful in situations where the error distribution has bounded support. In this paper, we derive the asymptotic distribution of this estimator in cases where the error distribution has bounded and unbounded support. We also ..."
Abstract
 Add to MetaCart
The Chebyshev or L ∞ estimator minimizes the maximum absolute residual and is useful in situations where the error distribution has bounded support. In this paper, we derive the asymptotic distribution of this estimator in cases where the error distribution has bounded and unbounded support. We also consider the asymptotics of setmembership estimators such as the Chebyshev centre and maximum inscribed ellipsoid estimators.
Asymptotic theory for Mestimators of bound aries
"... We consider some asymptotic distribution theory for Mestimators of the parameters of a linear model whose errors are nonnegative; these estimators are the solutions of constrained optimization problems and their asymptotic theory is nonstandard. Under weak conditions on the distribution of the er ..."
Abstract
 Add to MetaCart
(Show Context)
We consider some asymptotic distribution theory for Mestimators of the parameters of a linear model whose errors are nonnegative; these estimators are the solutions of constrained optimization problems and their asymptotic theory is nonstandard. Under weak conditions on the distribution of the errors and on the design, we show that a large class of estimators have the same asymptotic distributions in the case of i.i.d. errors; however, this invariance does not hold under noni.i.d. errors.