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44
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
Generalized Partially Linear SingleIndex Models
 Journal of the American Statistical Association
, 1998
"... The typical generalized linear model for a regression of a response Y on predictors (X; Z) has conditional mean function based upon a linear combination of (X; Z). We generalize these models to have a nonparametric component, replacing the linear combination T 0 X + T 0 Z by 0 ( T 0 X) + T 0 Z, wher ..."
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Cited by 63 (24 self)
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The typical generalized linear model for a regression of a response Y on predictors (X; Z) has conditional mean function based upon a linear combination of (X; Z). We generalize these models to have a nonparametric component, replacing the linear combination T 0 X + T 0 Z by 0 ( T 0 X) + T 0 Z, where 0 ( ) is an unknown function. We call these generalized partially linear singleindex models (GPLSIM). The models include the "singleindex" models, which have 0 = 0. Using local linear methods, estimates of the unknown parameters ( 0 ; 0 ) and the unknown function 0 ( ) are proposed, and their asymptotic distributions obtained. Examples illustrate the models and the proposed estimation methodology.
An MCMC approach to classical estimation
, 2003
"... This paper studies computationally and theoretically attractive estimators called here Laplace type estimators (LTEs), which include means and quantiles of quasiposterior distributions dened as transformations of general (nonlikelihoodbased) statistical criterion functions, such as those in GMM, n ..."
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Cited by 56 (8 self)
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This paper studies computationally and theoretically attractive estimators called here Laplace type estimators (LTEs), which include means and quantiles of quasiposterior distributions dened as transformations of general (nonlikelihoodbased) statistical criterion functions, such as those in GMM, nonlinear IV, empirical likelihood, and minimum distance methods. The approach generates an alternative to classical extremum estimation and also falls outside the parametric Bayesian approach. For example, it o ers a new attractive estimation method for such important semiparametric problems as censored and instrumental quantile regression, nonlinear GMM and valueatrisk models. The LTEs are computed using Markov Chain Monte Carlo methods, which help circumvent the computational curse of dimensionality. Alarge sample theory is obtained and illustrated for regular cases.
Testing and Comparing ValueatRisk Measures
, 2001
"... La valeur expose au risque (value at risk  VaR) est devenue un outil standard de mesure et de communication des risques associs aux marchs financiers. Plus de quatrevingts fournisseurs commerciaux proposent actuellement des systmes de gestion d'entreprise ou de gestion des risques commerciaux four ..."
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Cited by 25 (3 self)
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La valeur expose au risque (value at risk  VaR) est devenue un outil standard de mesure et de communication des risques associs aux marchs financiers. Plus de quatrevingts fournisseurs commerciaux proposent actuellement des systmes de gestion d'entreprise ou de gestion des risques commerciaux fournissant des mesures de type VaR. C'est donc souvent aux gestionnaires des risques qu'incombe la tche difficile d'oprer un choix parmi cette plthore de modles de risques. Cet article propose un cadre utile pour dterminer par quel moyen le gestionnaire des risques peut s'assurer que la mesure de VaR dont il dispose est bien dfinie, et, dans un deuxime temps, comparer deux mesures de VaR diffrentes et choisir la meilleure en s'appuyant sur des donnes statistiques utiles. Dans l'application, diffrentes mesures de VaR sont calcules partir soit de mesures de volatilit historiques ou de mesures de volatilit implicites dans le prix des options; les VaR sont galement vrifies et compares. ValueatR...
Quantile Autoregression
 Convergence of Stochastic Processes
, 2006
"... Abstract. We consider quantile autoregression (QAR) models in which the autoregressive coefficients can be expressed as monotone functions of a single, scalar random variable. The models can capture systematic influences of conditioning variables on the location, scale and shape of the conditional d ..."
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Cited by 18 (4 self)
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Abstract. We consider quantile autoregression (QAR) models in which the autoregressive coefficients can be expressed as monotone functions of a single, scalar random variable. The models can capture systematic influences of conditioning variables on the location, scale and shape of the conditional distribution of the response, and therefore constitute a significant extension of classical constant coefficient linear time series models in which the effect of conditioning is confined to a location shift. The models may be interpreted as a special case of the general random coefficient autoregression model with strongly dependent coefficients. Statistical properties of the proposed model and associated estimators are studied. The limiting distributions of the autoregression quantile process are derived. Quantile autoregression inference methods are also investigated. Empirical applications of the model to the U.S. unemployment rate and U.S. gasoline prices highlight the potential of the model. 1.
Variable selection in semiparametric regression modeling. Available at http://www.stat.psu.edu/˜rli/research/varyselTR.pdf
, 2005
"... In this paper, we are concerned with how to select significant variables in semiparametric modeling. Variable selection for semiparametric regression models consists of two components: model selection for nonparametric components and selection of significant variables for the parametric portion. Thu ..."
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Cited by 13 (3 self)
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In this paper, we are concerned with how to select significant variables in semiparametric modeling. Variable selection for semiparametric regression models consists of two components: model selection for nonparametric components and selection of significant variables for the parametric portion. Thus, semiparametric variable selection is much more challenging than parametric variable selection (e.g., linear and generalized linear models) because traditional variable selection procedures including stepwise regression and the best subset selection now require separate model selection for the nonparametric components for each submodel. This leads to a very heavy computational burden. In this paper, we propose a class of variable selection procedures for semiparametric regression models using nonconcave penalized likelihood. We establish the rate of convergence of the resulting estimate. With proper choices of penalty functions and regularization parameters, we show the asymptotic normality of the resulting estimate and further demonstrate that the proposed procedures perform as well as an oracle procedure. A semiparametric generalized likelihood ratio test is proposed to select significant variables in the nonparametric component. We investigate the asymptotic behavior of the proposed test and demonstrate that its limiting null distribution follows a chisquare distribution which is independent of the nuisance parameters. Extensive Monte Carlo simulation studies are conducted to examine the finite sample performance of the proposed variable selection procedures.
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...
Quantile Regression under Misspecification, with an Application to the U.S
 Wage Structure. Econometrica
, 2006
"... Quantile regression (QR) fits a linear model for conditional quantiles, just as ordinary least squares (OLS) fits a linear model for conditional means. An attractive feature of OLS is that it gives the minimum mean square error linear approximation to the conditional expectation function even when t ..."
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Cited by 12 (2 self)
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Quantile regression (QR) fits a linear model for conditional quantiles, just as ordinary least squares (OLS) fits a linear model for conditional means. An attractive feature of OLS is that it gives the minimum mean square error linear approximation to the conditional expectation function even when the linear model is misspecified. Empirical research using quantile regression with discrete covariates suggests that QR may have a similar property, but the exact nature of the linear approximation has remained elusive. In this paper, we show that QR minimizes a weighted meansquared error loss function for specification error. The weighting function is an average density of the dependent variable near the true conditional quantile. The weighted least squares interpretation of QR is used to derive an omitted variables bias formula and a partial quantile regression concept, similar to the relationship between partial regression and OLS. We also present asymptotic theory for the QR process under misspecification of the conditional quantile function. The approximation properties of QR are illustrated using wage data from the US census. These results point to major changes in inequality from 19902000.
2003), “Estimation, Inference, and Specification Testing for Possibly Misspecified Quantile Regression
 Maximum Likelihood Esitmation of Misspecified Models: Twenty Years Later, 107–132
"... Abstract: To date the literature on quantile regression and least absolute deviation regression has assumed either explicitly or implicitly that the conditional quantile regression model is correctly specified. When the model is misspecified, confidence intervals and hypothesis tests based on the co ..."
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Cited by 9 (1 self)
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Abstract: To date the literature on quantile regression and least absolute deviation regression has assumed either explicitly or implicitly that the conditional quantile regression model is correctly specified. When the model is misspecified, confidence intervals and hypothesis tests based on the conventional covariance matrix are invalid. Although misspecification is a generic phenomenon and correct specification is rare in reality, there has to date been no theory proposed for inference when a conditional quantile model may be misspecified. In this paper, we allow for possible misspecification of a linear conditional quantile regression model. We obtain consistency of the quantile estimator for certain “pseudotrue ” parameter values and asymptotic normality of the quantile estimator when the model is misspecified. In this case, the asymptotic covariance matrix has a novel form, not seen in earlier work, and we provide a consistent estimator of the asymptotic covariance matrix. We also propose a quick and simple test for conditional quantile misspecification based on the quantile residuals.