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Testing a Parametric Model Against a Semiparametric Alternative

Published online by Cambridge University Press:  11 February 2009

Joel L. Horowitz  and
Wolfgang Härdle
Joel L. Horowitz
Affiliation:
University of Iowa
Wolfgang Härdle
Affiliation:
Institut für Statistik und Ökonometrie Humboldt Universität zu Berlin
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Abstract

This paper describes a method for testing a parametric model of the mean of a random variable Y conditional on a vector of explanatory variables X against a semiparametric alternative. The test is motivated by a conditional moment test against a parametric alternative and amounts to replacing the parametric alternative model with a semiparametric model. The resulting semiparametric test is consistent against a larger set of alternatives than are parametric conditional moments tests based on finitely many moment conditions. The results of Monte Carlo experiments and an application illustrate the usefulness of the new test.

Type
Articles
Information
Econometric Theory , Volume 10 , Issue 5 , December 1994 , pp. 821 - 848
Copyright
Copyright © Cambridge University Press 1994

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References

1Bierens, H.J. Kernel estimators of regression functions. In Bewley, T.F. (ed.), Advances in Econometrics: Fifth World Congress, vol. 1, pp. 99–144. New York: Cambridge University Press, 1987.CrossRefGoogle Scholar
2Bierens, H.J.A consistent conditional moment test of functional form. Econometrka 58 (1990): 1443–1458.CrossRefGoogle Scholar
3Eubank, R.L. & Spiegelman, C.H.. Testing the goodness of fit of a linear model via non-parametric regression. Journal of the American Statistical Association 85 (1990): 387–392.CrossRefGoogle Scholar
4Gozalo, P.L.A consistent model specification test for nonparametric estimation of regression function models. Econometric Theory 9 (1993): 451–477.CrossRefGoogle Scholar
5Hall, P.Central limit theorem for integrated square error of multivariate nonparametric density estimators. Journal of Multivariate Analysis 14 (1984): 1–16.CrossRefGoogle Scholar
6Hardle, W.A note on jackknifing kernel regression function estimators. IEEE Transactions of Information Theory 32 (1986): 298–300.CrossRefGoogle Scholar
7Härdle, W.Applied Nonparametric Regression. New York: Cambridge University Press, 1990.CrossRefGoogle Scholar
8Härdle, W. & Mammen, E.. Comparing nonparametric versus parametric regression fits. Annals of Statistics 21 (1993): 1926–1947.CrossRefGoogle Scholar
9Hong, Y. & White, H.. Consistent Specification Testing via Nonparametric Series Regression. Discussion paper, Department of Economics, University of California, San Diego, CA, 1992.Google Scholar
10Horowitz, J.L.Semiparametric estimation of a work-trip mode choice model. Journal of Econometrics 58 (1993): 49–70.CrossRefGoogle Scholar
11Huber, P.J.Projection pursuit. The Annals of Statistics 13 (1985): 435–475.Google Scholar
12le Cessie, S. & van Houwelingen, J.C.. A goodness-of-fit test for binary regression models, based on smoothing methods. Biometrics 47 (1991): 1267–1282.CrossRefGoogle Scholar
13Nelson, F.D. & Savin, N.E.. The danger of extrapolating asymptotic local power. Econometrica 58 (1990): 977–981.CrossRefGoogle Scholar
14Newey, W.K.Maximum likelihood specification testing and conditional moment tests. Econometrica 53 (1985): 1047–1070.CrossRefGoogle Scholar
15Pollard, D.Convergence of Stochastic Processes. New York: Springer-Verlag, 1984.CrossRefGoogle Scholar
16Schucany, W.R. & Sommers, J.P.. Improvement of kernel type density estimators. Journal of the American Statistical Association 72 (1977): 420–423.CrossRefGoogle Scholar
17Serfling, R.J.Approximation Theorems of Mathematical Statistics. New York: John Wiley & Sons, 1980.CrossRefGoogle Scholar
18Silverman, B.W.Weak and strong uniform consistency of the kernel estimate of a density and its derivatives. The Annals of Statistics 6 (1978): 177–184.CrossRefGoogle Scholar
19Whang, Y.-J. & Andrews, D.W.K.. Tests of Specification for Parametric and Semiparametric Models. Cowles Foundation discussion paper #968, Yale University, New Haven, CT, 1991.Google Scholar
20Wooldridge, J.M.A test for functional form against nonparametric alternatives. Econometric Theory 8 (1992): 452–475.CrossRefGoogle Scholar
21Yatchew, A.J.Nonparametric regression tests based on least squares. Econometric Theory 8 (1992): 435–451.CrossRefGoogle Scholar
22Zheng, X. A consistent test of functional form via nonparametric estimation techniques. Discussion paper, Department of Economics, Princeton University, Princeton, NJ, 1991.Google Scholar