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174
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 254 (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 238 (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 175 (2 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 56 (15 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.
Exact and approximate stepdown methods for multiple hypothesis testing
 Journal o f the American Statistical Association
, 2005
"... Consider the problem of testing k hypotheses simultaneously. In this article we discuss finite and largesample theory of stepdown methods that provide control of the familywise error rate (FWE). To improve on the Bonferroni method or on Holm’s stepdown method, Westfall and Young made effective use ..."
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Cited by 55 (8 self)
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Consider the problem of testing k hypotheses simultaneously. In this article we discuss finite and largesample theory of stepdown methods that provide control of the familywise error rate (FWE). To improve on the Bonferroni method or on Holm’s stepdown method, Westfall and Young made effective use of resampling to construct stepdown methods that implicitly estimate the dependence structure of the test statistics. However, their methods depend on an assumption known as “subset pivotality. ” Our goal here is to construct general stepdown methods that do not require such an assumption. To accomplish this, we take a close look at what makes stepdown procedures work; a key component is a monotonicity requirement of critical values. By imposing monotonicity on estimated critical values (which is not an assumption on the model but rather is an assumption on the method), we show how to construct stepdown tests that can be applied in a stagewise fashion so that at most k tests need to be computed. Moreover, at each stage, an intersection test that controls the usual probability of a type 1 error is calculated, which allows us to draw on an enormous resampling literature as a general means of test construction. In addition, it is possible to carry out this method using the same set of resamples (or subsamples) for each of the intersection tests.
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 ..."
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Cited by 46 (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
"... We 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. T ..."
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Cited by 46 (24 self)
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We 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.
Control of generalized error rates in multiple testing
 IEW  WORKING PAPERS IEWWP245, INSTITUTE FOR EMPIRICAL RESEARCH IN ECONOMICS  IEW (2005) AVAILABLE AT HTTP://IDEAS.REPEC.ORG/P/ZUR/IEWWPX/245.HTML
, 2005
"... Consider the problem of testing s hypotheses simultaneously. The usual approach to dealing with the multiplicity problem is to restrict attention to procedures that control the probability of even one false rejection, the familiar familywise error rate (FWER). In many applications, particularly if s ..."
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Cited by 35 (6 self)
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Consider the problem of testing s hypotheses simultaneously. The usual approach to dealing with the multiplicity problem is to restrict attention to procedures that control the probability of even one false rejection, the familiar familywise error rate (FWER). In many applications, particularly if s is large, one might be willing to tolerate more than one false rejection if the number of such cases is controlled, thereby increasing the ability of the procedure to reject false null hypotheses One possibility is to replace control of the FWER by control of the probability of k or more false rejections, which is called the kFWER. We derive both singlestep and stepdown procedures that control the kFWER in finite samples or asymptotically, depending on the situation. Lehmann and Romano (2005a) derive some exact methods for this purpose, which apply whenever pvalues are available for individual tests; no assumptions are made on the joint dependence of the pvalues. In contrast, we construct methods that implicitly take into account the dependence structure of the individual test statistics in order to further increase the ability to detect false null hypotheses. We also consider the false discovery proportion (FDP) defined as the number of false rejections divided by the total number of rejections (and defined to be 0 if there are no rejections). The false discovery rate proposed by Benjamini and Hochberg (1995) controls E(FDP). Here, the goal is to construct methods which satisfy, for a given γ and α, P {FDP> γ} ≤ α, at least asymptotically.
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 34 (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
Instrumental Variable Estimation of a Threshold Model,” Econometric Theory
, 2004
"... Threshold models ~sample splitting models! have wide application in economics+ Existing estimation methods are confined to regression models, which require that all righthandside variables are exogenous+ This paper considers a model with endogenous variables but an exogenous threshold variable+ We ..."
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Cited by 32 (1 self)
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Threshold models ~sample splitting models! have wide application in economics+ Existing estimation methods are confined to regression models, which require that all righthandside variables are exogenous+ This paper considers a model with endogenous variables but an exogenous threshold variable+ We develop a twostage least squares estimator of the threshold parameter and a generalized method of moments estimator of the slope parameters+ We show that these estimators are consistent, and we derive the asymptotic distribution of the estimators+ The threshold estimate has the same distribution as for the regression case ~Hansen, 2000, Econometrica 68, 575–603!, with a different scale+ The slope parameter estimates are asymptotically normal with conventional covariance matrices+ We investigate our distribution theory with a Monte Carlo simulation that indicates the applicability of the methods+ 1.