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24
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 69 (11 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 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 66 (11 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 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 55 (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
Model specification testing in nonparametric and semiparametric regression. Working paper available at www.maths.uwa.edu.au/˜jiti/jems.pdf
, 2005
"... Abstract. This paper considers two classes of semiparametric nonlinear regression models, in which nonlinear components are introduced to reflect the nonlinear fluctuation in the mean. A general estimation and testing procedure for nonparametric time series regression under the α–mixing condition i ..."
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Cited by 11 (5 self)
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Abstract. This paper considers two classes of semiparametric nonlinear regression models, in which nonlinear components are introduced to reflect the nonlinear fluctuation in the mean. A general estimation and testing procedure for nonparametric time series regression under the α–mixing condition is introduced. Several test statistics for testing nonparametric significance, linearity and additivity in nonparametric and semiparametric time series econometric models are then constructed. The proposed test statistics are shown to have asymptotic normal distributions under their respective null hypotheses. Moreover, the proposed testing procedures are illustrated by several simulated examples. In addition, one of the proposed testing procedures is applied to a continuoustime model and implemented through a set of the US Federal interest rate data. Our research suggests that it is unreasonable to assume the linearity in the drift for the given data as required by some existing studies.
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 10 (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 ...
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 10 (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.
Nonparametric bootstrap tests for neglected nonlinearity in time series regression models," Manuscript
, 1999
"... Various nonparametric kernel regression estimators are presented, based on which we consider two nonparametric tests for neglected nonlinearity in time series regression models. One of them is the goodnessoffit test of Cai, Fan, and Yao (2000) and another is the nonparametric conditional moment te ..."
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Cited by 5 (1 self)
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Various nonparametric kernel regression estimators are presented, based on which we consider two nonparametric tests for neglected nonlinearity in time series regression models. One of them is the goodnessoffit test of Cai, Fan, and Yao (2000) and another is the nonparametric conditional moment test by Li and Wang (1998) and Zheng (1996). Bootstrap procedures are used for these tests and their performance is examined via monte carlo experiments, especially with conditionally heteroskedastic errors. Key Words: nonparametric test, nonlinearity, time series, functionalcoefficient model, conditional moment test, naive bootstrap, wild bootstrap, conditional heteroskedasticity, GARCH, monte carlo. ∗We would like to thank Zongwu Cai, Jianqing Fan, Qi Li, an anonymous referee, and Associate Editor for their helpful comments which greatly improved the paper and/or for sharing their programs. All errors are our own. Lee thanks UC Regents’s Faculty Fellowship and Faculty Development Awards, and Ullah thanks the Academic Senate of UCR for the research support. 1
Consistent Specification Testing for Conditional Moment Restrictions
"... This paper introduces specification tests of conditional moment restrictions. The proposed tests are generalizations of the KolmogorovSmirnov and Cramervon Mises tests and they are consistent against all alternatives to the null hypothesis, powerful against 1= p n local alternatives and not depend ..."
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Cited by 4 (0 self)
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This paper introduces specification tests of conditional moment restrictions. The proposed tests are generalizations of the KolmogorovSmirnov and Cramervon Mises tests and they are consistent against all alternatives to the null hypothesis, powerful against 1= p n local alternatives and not dependent on any smoothing parameter. A nonparametric bootstrap procedure based on recentered criterion function is suggested to obtain critical values for the tests and is justified asymptotically.
Weighted Simulated Integrated Conditional Moment Tests for Parametric Conditional Distributions of Stationary Time Series Processes
, 2013
"... In this paper we propose a weighted simulated integrated conditional moment (WSICM) test of the validity of parametric specifications of conditional distribution models for stationary time series data, by combining the weighted ICM test of Bierens (1984) for time series regression models with the Si ..."
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In this paper we propose a weighted simulated integrated conditional moment (WSICM) test of the validity of parametric specifications of conditional distribution models for stationary time series data, by combining the weighted ICM test of Bierens (1984) for time series regression models with the Simulated ICM test of Bierens and Wang (2012) of conditional distribution models for crosssection data. To the best of our knowledge no other consistent test for parametric conditional time series distributions has been proposed yet in the literature, despite consistency claims made by some authors. Professor Emeritus of Economics. Please address correspondence by email only to hbierens@psu.edu, as I no longer have an office at Penn State. 1 1