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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 138 (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
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 a sequence ..."
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Cited by 12 (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...
Asymptotics for L_1estimators of regression parameters under heteroscedasticity
 Canadian Journal of Statistics
, 1999
"... : We consider the asymptotic behaviour of L 1 estimators in a linear regression under a very general form of heteroscedasticity. The limiting distributions of the estimators are derived under standard conditions on the design. We also consider the asymptotic behaviour of the bootstrap in the hetero ..."
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Cited by 3 (0 self)
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: We consider the asymptotic behaviour of L 1 estimators in a linear regression under a very general form of heteroscedasticity. The limiting distributions of the estimators are derived under standard conditions on the design. We also consider the asymptotic behaviour of the bootstrap in the heteroscedastic model and show that it is consistent to first order only if the limiting distribution is Normal. R' esum' e: L'auteur 'etudie le comportement asymptotique d'estimateurs L 1 dans le cadre de la r'egression lin'eaire, sous des hypoth`eses d'h'et'erosc'edasticit'e tr`es g'en'erales. Il d'etermine leur loi limite dans des conditions classiques portant sur la matrice d'incidence. Il examine en outre le comportement asymptotique du bootstrap dans le mod`ele h'et'erosc'edastique et montre que la convergence du premier ordre ne se produit que si la loi limite est gaussienne. Key words and phrases: linear regression, L 1 estimation, heteroscedasticity, asymptotic distribution, bootstrap. ...