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23
Consistent Specification Testing With Nuisance Parameters Present Only Under The Alternative
, 1995
"... . The nonparametric and the nuisance parameter approaches to consistently testing statistical models are both attempts to estimate topological measures of distance between a parametric and a nonparametric fit, and neither dominates in experiments. This topological unification allows us to greatly ex ..."
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Cited by 55 (10 self)
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. The nonparametric and the nuisance parameter approaches to consistently testing statistical models are both attempts to estimate topological measures of distance between a parametric and a nonparametric fit, and neither dominates in experiments. This topological unification allows us to greatly extend the nuisance parameter approach. How and why the nuisance parameter approach works and how it can be extended bears closely on recent developments in artificial neural networks. Statistical content is provided by viewing specification tests with nuisance parameters as tests of hypotheses about Banachvalued random elements and applying the Banach Central Limit Theorem and Law of Iterated Logarithm, leading to simple procedures that can be used as a guide to when computationally more elaborate procedures may be warranted. 1. Introduction In testing whether or not a parametric statistical model is correctly specified, there are a number of apparently distinct approaches one might take. T...
EMPIRICAL LIKELIHOOD METHODS IN ECONOMETRICS: THEORY AND PRACTICE
, 2006
"... Recent developments in empirical likelihood (EL) methods are reviewed. First, to put the method in perspective, two interpretations of empirical likelihood are presented, one as a nonparametric maximum likelihood estimation method (NPMLE) and the other as a generalized minimum contrast estimator ( ..."
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Cited by 18 (2 self)
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Recent developments in empirical likelihood (EL) methods are reviewed. First, to put the method in perspective, two interpretations of empirical likelihood are presented, one as a nonparametric maximum likelihood estimation method (NPMLE) and the other as a generalized minimum contrast estimator (GMC). The latter interpretation provides a clear connection between EL, GMM, GEL and other related estimators. Second, EL is shown to have various advantages over other methods. The theory of large deviations demonstrates that EL emerges naturally in achieving asymptotic optimality both for estimation and testing. Interestingly, higher order asymptotic analysis also suggests that EL is generally a preferred method. Third, extensions of EL are discussed in various settings, including estimation of conditional moment restriction models, nonparametric specification testing and time series models. Finally, practical issues in applying EL to real data, such as computational algorithms for EL, are discussed. Numerical examples to illustrate the efficacy of the method are presented.
An Adaptive, RateOptimal Test Of A Parametric Model . . .
, 1999
"... We develop a new test of a parametric model of a conditional mean function against a nonparametric alternative. The test adapts to the unknown smoothness of the alternative model and is uniformly consistent against alternatives whose distance from the parametric model converges to zero at the fastes ..."
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Cited by 9 (0 self)
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We develop a new test of a parametric model of a conditional mean function against a nonparametric alternative. The test adapts to the unknown smoothness of the alternative model and is uniformly consistent against alternatives whose distance from the parametric model converges to zero at the fastest possible rate. This rate is slower than n1/2. Some existing tests have nontrivial power against restricted classes of alternatives whose distance from the parametric model decreases at the rate n1/2. There are, however, sequences of alternatives against which these tests are inconsistent and ours is consistent. As a consequence, there are alternative models for which the finitesample power of our test greatly exceeds that of existing tests. This conclusion is illustrated by the results of some Monte Carlo experiments.
An Adaptive, RateOptimal Test Of Linearity For Median Regression Models
, 2002
"... This paper is concerned with testing the hypothesis that a conditional median function is linear against a nonparametric alternative with unknown smoothness. We develop a test that is uniformly consistent against alternatives whose distance from the linear model converges to zero at the fastest poss ..."
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Cited by 9 (1 self)
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This paper is concerned with testing the hypothesis that a conditional median function is linear against a nonparametric alternative with unknown smoothness. We develop a test that is uniformly consistent against alternatives whose distance from the linear model converges to zero at the fastest possible rate. The test accommodates conditional heteroskedasticity of unknown form. The numerical performance and usefulness of the test are illustrated by the results of Monte Carlo experiments and an empirical example. Key words: Hypothesis testing, local alternative, uniform consistency We thank Russell Davidson and Jianqing Fan for helpful comments. The research of Joel L. Horowitz was supported in part by NSF Grant SES9910925 and the Alexander von Humboldt Foundation. 1 AN ADAPTIVE, RATEOPTIMAL TEST OF LINEARITY FOR MEDIAN REGRESSION MODELS 1. INTRODUCTION This paper is concerned with testing a linear medianregression model against a nonparametric alternative. We develop a test that ...
Estimating residual variance in nonparametric regression using least squares, Biometrika 92: 821–830
, 2005
"... We propose a new estimator for the error variance in a nonparametric regression model. We estimate the error variance as the intercept in a simple linear regression model with squared differences of paired observations as the dependent variable and squared distances between the paired covariates as ..."
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Cited by 8 (4 self)
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We propose a new estimator for the error variance in a nonparametric regression model. We estimate the error variance as the intercept in a simple linear regression model with squared differences of paired observations as the dependent variable and squared distances between the paired covariates as the regressor. Our method can be applied to nonparametric regression models with multivariate functions defined on arbitrary subsets of normed spaces, possibly observed on unequally spaced or clustered designed points. No ordering is required for our method. We develop methods for selecting the bandwidth. For the special case of one dimensional domain with equally spaced design points, we show that our method reaches an asymptotic optimal rate which is not achieved by some existing methods. We conduct extensive simulations to evaluate finite sample performance of our method and compare it with existing methods. We illustrate our method using a real data set.
Nonparametric Checks For SingleIndex Models
 Ann. Statist
, 2005
"... In this paper we study goodnessoffit testing of singleindex models. The large sample behavior of certain scoretype test statistics is investigated. As a byproduct, we obtain asymptotically distributionfree maximin tests for a large class of local alternatives. Furthermore, characteristic functi ..."
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Cited by 8 (3 self)
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In this paper we study goodnessoffit testing of singleindex models. The large sample behavior of certain scoretype test statistics is investigated. As a byproduct, we obtain asymptotically distributionfree maximin tests for a large class of local alternatives. Furthermore, characteristic function based goodnessoffit tests are proposed which are omnibus and able to detect peak alternatives. Simulation results indicate that the approximation through the limit distribution is acceptable already for moderate sample sizes. Applications to two real data sets are illustrated. 1. Introduction. Suppose
An adaptive empirical likelihood test for parametric time series regression models
 J. R. STATIST. SOC.  SERIES B
, 2006
"... A test for a parametric regression model against a sequence of local alternative is constructed based on an empirical likelihood test statistic that measures the goodnessoffit between the parametric model and its nonparametric counterpart. To reduce the dependence of the test on a single smoothing ..."
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Cited by 7 (5 self)
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A test for a parametric regression model against a sequence of local alternative is constructed based on an empirical likelihood test statistic that measures the goodnessoffit between the parametric model and its nonparametric counterpart. To reduce the dependence of the test on a single smoothing bandwidth, the test is formulated by maximizing a standardized version of the empirical likelihood test statistic over a set of smoothing bandwidths. It is demonstrated that the proposed test is able to distinguish local alternatives from the null hypothesis at an optimal rate.
Consistent Specification Tests for Semiparametric/Nonparametric Models Based on Series . . .
 JOURNAL OF ECONOMETRICS
, 2003
"... This paper considers the problem of consistent model specification tests using series estimation methods. The null models we consider in this paper all contain some nonparametric components. A leading case we consider is to test for an additive partially linear model. The null distribution of the ..."
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Cited by 7 (0 self)
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This paper considers the problem of consistent model specification tests using series estimation methods. The null models we consider in this paper all contain some nonparametric components. A leading case we consider is to test for an additive partially linear model. The null distribution of the test statistic is derived using a central limit theorem for Hilbert valued random arrays. The test statistic is shown to be able to detect local alternatives that approach the null models at the order of O p (n 1/2 ). We suggest to use the wild bootstrap method to approximate the critical values of the test. A small Monte Carlo simulation is reported to examine the finite sample performance of the proposed test. We also show
SIMULTANEOUS CONFIDENCE BANDS FOR NONPARAMETRIC REGRESSION WITH REPEATED MEASUREMENTS DATA
, 908
"... Abstract. We look into nonparametric regression with repeated measurements collected on a fine grid. An asymptotic normality result is obtained in a function space equipped with the supremum norm. This result can be used to build simultaneous confidence bands (SCB) for various tasks in statistical e ..."
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Cited by 3 (0 self)
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Abstract. We look into nonparametric regression with repeated measurements collected on a fine grid. An asymptotic normality result is obtained in a function space equipped with the supremum norm. This result can be used to build simultaneous confidence bands (SCB) for various tasks in statistical exploration, estimation and inference. Two applications are proposed: one is a SCB procedure for the regression function whose accuracy improves upon other available methods, and the other is a goodnessoffit test having the ability to detect local departures from a parametric regression shape, as opposed to the usual goodnessoffit tests which only track global departures. A numerical study is also provided. 1.
2005): \Consistent Tests of Conditional Moment Restrictions." Forthcoming in Annales d'Economie et de Statistique
"... We address the issue of building consistent specification tests in econometric models defined through multiple conditional moment restrictions. In this aim, we extend the two methodologies developed for testing the parametric specification of a regression function to testing general conditional mome ..."
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Cited by 2 (0 self)
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We address the issue of building consistent specification tests in econometric models defined through multiple conditional moment restrictions. In this aim, we extend the two methodologies developed for testing the parametric specification of a regression function to testing general conditional moment restrictions. Two classes of tests are proposed, which can be both interpreted as Mtests based on integrated conditional moment restrictions. The first class depends upon nonparametric functions that are estimated by kernel smoothers. The second type of test is built as a functional of a marked empirical process. For both tests, a simulation procedure for obtaining critical values is shown to be asymptotically valid. Comparison of finite sample performances of the tests are investigated by means of several MonteCarlo experiments.