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97
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 137 (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
Sample Splitting and Threshold Estimation
 Econometrica
, 2000
"... Threshold models have a wide variety of applications in economics. Direct applications include models of separating and multiple equilibria. Other applications include empirical sample splitting when the sample split is based on a continuouslydistributed variable such as firm size. In addition, thr ..."
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Cited by 84 (3 self)
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Threshold models have a wide variety of applications in economics. Direct applications include models of separating and multiple equilibria. Other applications include empirical sample splitting when the sample split is based on a continuouslydistributed variable such as firm size. In addition, threshold models may be used as a parsimonious strategy for nonparametric function estimation. For example, the threshold autoregressive model Ž TAR. is popular in the nonlinear time series literature. Threshold models also emerge as special cases of more complex statistical frameworks, such as mixture models, switching models, Markov switching models, and smooth transition threshold models. It may be important to understand the statistical properties of threshold models as a preliminary step in the development of statistical tools to handle these more complicated structures. Despite the large number of potential applications, the statistical theory of threshold estimation is undeveloped. It is known that threshold estimates are superconsistent, but a distribution theory useful for testing and inference has yet to be provided. This paper develops a statistical theory for threshold estimation in the regression context. We allow for either crosssection or time series observations. Least squares estimation of the regression parameters is considered. An asymptotic distribution theory for the regression estimates Ž the threshold and the regression slopes. is developed. It is found that the distribution of the threshold estimate is nonstandard. A method to construct asymptotic confidence intervals is developed by inverting the likelihood ratio statistic. It is shown that this yields asymptotically conservative confidence regions. Monte Carlo simulations are presented to assess the accuracy of the asymptotic approximations. The empirical relevance of the theory is illustrated through an application to the multiple equilibria growth model of Durlauf and Johnson Ž 1995..
The bootstrap
 In Handbook of Econometrics
, 2001
"... The bootstrap is a method for estimating the distribution of an estimator or test statistic by resampling one’s data. It amounts to treating the data as if they were the population for the purpose of evaluating the distribution of interest. Under mild regularity conditions, the bootstrap yields an a ..."
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Cited by 73 (1 self)
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The bootstrap is a method for estimating the distribution of an estimator or test statistic by resampling one’s data. It amounts to treating the data as if they were the population for the purpose of evaluating the distribution of interest. Under mild regularity conditions, the bootstrap yields an approximation to the distribution of an estimator or test statistic that is at least as accurate as the
Computing Chernoff’s distribution
 J. Comput. Graph. Statist
"... A distribution that arises in problems of estimation of monotone functions is that of the location of the maximum of twosided Brownian motion minus a parabola. Using results from the � rst author’s earlier work, we present algorithms and programs for computation of this distribution and its quantil ..."
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Cited by 35 (12 self)
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A distribution that arises in problems of estimation of monotone functions is that of the location of the maximum of twosided Brownian motion minus a parabola. Using results from the � rst author’s earlier work, we present algorithms and programs for computation of this distribution and its quantiles. We also present some comparisons with earlier computations and simulations.
Efficient Estimation for the Proportional Hazards Model with "Case 2" Interval Censoring
, 1995
"... Maximum likelihood estimation for the proportional hazards model with interval censored data is considered. The estimators are computed by profile likelihood methods using Groeneboom's iterative convex minorant algorithm. Under appropriate regularity conditions, the maximum likelihood estimator for ..."
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Cited by 32 (5 self)
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Maximum likelihood estimation for the proportional hazards model with interval censored data is considered. The estimators are computed by profile likelihood methods using Groeneboom's iterative convex minorant algorithm. Under appropriate regularity conditions, the maximum likelihood estimator for the regression parameter is shown to be asymptotically normal and efficient. Two approaches for estimation of the variancecovariance matrix for the estimated regression parameter are proposed: one uses the inverse of the observed information matrix, another uses the curvature of the profile likelihood function. An example is given to illustrate the proposed methods.
Likelihood ratio tests for monotone functions
 Ann. Statist
, 2001
"... \Ve study the problem of testing for equality at a fixed point in the setting of nonparametric estimation of a monotone function. The likelihood ratio test for this hypothesis is derived in the particular case of interval censoring (or current status data) and its limiting distribution is obtained. ..."
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Cited by 28 (18 self)
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\Ve study the problem of testing for equality at a fixed point in the setting of nonparametric estimation of a monotone function. The likelihood ratio test for this hypothesis is derived in the particular case of interval censoring (or current status data) and its limiting distribution is obtained. The limiting distribution is that of the integral of the difference of the squared slope processes corresponding to a canonical version of the problem involving Brownian motion + t2 and greatest convex minorants thereof. 2ROI AI291968
Estimation of a monotone density or monotone hazard under random censoring
, 1993
"... JSTOR is a notforprofit service that helps scholars, researchers, and students discover, use, and build upon a wide range of content in a trusted digital archive. We use information technology and tools to increase productivity and facilitate new forms ..."
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Cited by 17 (5 self)
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JSTOR is a notforprofit service that helps scholars, researchers, and students discover, use, and build upon a wide range of content in a trusted digital archive. We use information technology and tools to increase productivity and facilitate new forms
Asymptotic Distributions Of The Maximal Depth Estimators For Regression And Multivariate Location
 Ann. Statist
, 1998
"... This paper completes the extension to higher dimensions for both regression and multivariate location models. 1 ..."
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Cited by 15 (1 self)
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This paper completes the extension to higher dimensions for both regression and multivariate location models. 1
GMM with many moment conditions
 Econometrica
, 2006
"... This paper provides a first order asymptotic theory for generalized method of moments (GMM) estimators when the number of moment conditions is allowed to increase with the sample size and the moment conditions may be weak. Examples in which these asymptotics are relevant include instrumental variabl ..."
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Cited by 14 (1 self)
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This paper provides a first order asymptotic theory for generalized method of moments (GMM) estimators when the number of moment conditions is allowed to increase with the sample size and the moment conditions may be weak. Examples in which these asymptotics are relevant include instrumental variable (IV) estimation with many (possibly weak or uninformed) instruments and some panel data models that cover moderate time spans and have correspondingly large numbers of instruments. Under certain regularity conditions, the GMM estimators are shown to converge in probability but not necessarily to the true parameter, and conditions for consistent GMM estimation are given. A general framework for the GMM limit distribution theory is developed based on epiconvergence methods. Some illustrations are provided, including consistent GMM estimation of a panel model with time varying individual effects, consistent limited information maximum likelihood estimation as a continuously updated GMM estimator, and consistent IV structural estimation using large numbers of weak or irrelevant instruments. Some simulations are reported.