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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...
Consistent Model Specification Tests
 Journal of Econometrics
, 1982
"... This paper reviews the literature on tests for the correct specification of the functional form of parametric conditional expectation and conditional distribution models. In particular I will discuss various versions of the Integrated Conditional Moment (ICM) test and the ideas behind them. 1 ..."
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Cited by 49 (10 self)
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This paper reviews the literature on tests for the correct specification of the functional form of parametric conditional expectation and conditional distribution models. In particular I will discuss various versions of the Integrated Conditional Moment (ICM) test and the ideas behind them. 1
Consistent Specification Testing Via Nonparametric Series Regression
 Econometrica
, 1995
"... This paper proposes two consistent onesided specification tests for parametric regression models, one based on the sample covariance between the residual from the parametric model and the discrepancy between the parametric and nonparametric fitted values; the other based on the difference in sum ..."
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Cited by 34 (3 self)
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This paper proposes two consistent onesided specification tests for parametric regression models, one based on the sample covariance between the residual from the parametric model and the discrepancy between the parametric and nonparametric fitted values; the other based on the difference in sums of squared residuals between the parametric and nonparametric models. We estimate the nonparametric model by series regression
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 ...
Feasible Multivariate Nonparametric Regression Estimation Using Weak Separability
, 1999
"... One of the main practical problems of nonparametric regression estimation is the curse of dimensionality. The curse of dimensionality arises because nonparametric regression estimates are dependent variable averages local to the point at which the regression function is to be estimated. The number o ..."
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One of the main practical problems of nonparametric regression estimation is the curse of dimensionality. The curse of dimensionality arises because nonparametric regression estimates are dependent variable averages local to the point at which the regression function is to be estimated. The number of observations `local' to the point of estimation decreases exponentially with the number of dimensions. The consequence is that the variance of unconstrained nonparametric regression estimators of multivariate regression functions is often so great that the unconstrained nonparametric regression estimates are of no practical use. In this paper I propose a new estimation method of weakly separable multivariate nonparametric regression functions. Weak separability is a weaker condition than required by other dimensionreduction techniques, although similar asymptotic variance reductions obtain. Indeed, weak separability is weaker than generalized additivity (see Hardle and Linton, 1996 and H...
Integrated Conditional Moment Tests for Parametric Conditional Distributions ∗
, 2011
"... In this paper we propose consistent integrated ionditional ioment tests for the validity of parametric conditional distribution models, based on the integrated squared difference between the empirical characteristic function of the actual data and the characteristic function implied by the model. To ..."
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In this paper we propose consistent integrated ionditional ioment tests for the validity of parametric conditional distribution models, based on the integrated squared difference between the empirical characteristic function of the actual data and the characteristic function implied by the model. To avoid numerical evaluation of the conditional characteristic function of the model distribution, a simulated integrated conditional moment test is proposed. As an empirical application we test the validity of a few common health economic count data models.
and
"... This paper develops a consistent test for the correct hazard rate specification within the context of random right hand censoring of the dependent variable. The test is based on comparing a parametric estimate with a kernel estimate of the hazard rate. We establish the asymptotic distribution of the ..."
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This paper develops a consistent test for the correct hazard rate specification within the context of random right hand censoring of the dependent variable. The test is based on comparing a parametric estimate with a kernel estimate of the hazard rate. We establish the asymptotic distribution of the test statistic under the null hypothesis of correct parametric specification of the hazard rate and establish the consistency of the test. c ○ 2001 Peking University Press
unknown title
, 2000
"... www.elsevier.com/locate/econbase Consistent specification testing for conditional moment restrictions a,b, ..."
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www.elsevier.com/locate/econbase Consistent specification testing for conditional moment restrictions a,b,