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INTEGRATED CONDITIONAL MOMENT TESTS FOR PARAMETRIC CONDITIONAL DISTRIBUTIONS

Published online by Cambridge University Press:  02 August 2011

Herman J. Bierens  and
Li Wang
Herman J. Bierens*
Affiliation:
Pennsylvania State University
Li Wang
Affiliation:
Penn State College of Medicine
*
*Address correspondence to Herman J. Bierens, Department of Economics and CAPCP, Pennsylvania State University, 510 Kern Graduate Building, University Park, PA 16802, USA; e-mail: hbierens@psu.edu.
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Abstract

In this paper we propose consistent integrated conditional moment 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.

Type
ARTICLES
Information
Econometric Theory , Volume 28 , Issue 2 , April 2012 , pp. 328 - 362
Copyright
Copyright © Cambridge University Press 2011

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References

REFERENCES

Andrews, D.W. (1997) A conditional Kolmogorov test. Econometrica 65, 1097–1128.CrossRefGoogle Scholar
Athreya, K.B. (1987) Bootstrap of the mean in the infinite variance case. Annals of Statistics 15, 724–731.CrossRefGoogle Scholar
Bickel, P. & Freedman, D. (1981) Some asymptotic theory for the bootstrap. Annals of Statistics 9, 1196–1217.CrossRefGoogle Scholar
Bierens, H.J. (1982) Consistent model specification tests. Journal of Econometrics 20, 105–134.CrossRefGoogle Scholar
Bierens, H.J. (1990) A consistent conditional moment test of functional form. Econometrica 58, 1443–1458.CrossRefGoogle Scholar
Bierens, H.J. (2004) Introduction to the Mathematical and Statistical Foundations of Econometrics. Cambridge University Press.CrossRefGoogle Scholar
Bierens, H.J. (2010) EasyReg International. Free econometrics software downloadable fromhttp://econ.la.psu.edu/∼hbierens/EASYREG.HTM.Google Scholar
Bierens, H.J. & Carvalho, J.R. (2007) Semi-nonparametric competing risks analysis of recidivism. Journal of Applied Econometrics 22, 971–993.CrossRefGoogle Scholar
Bierens, H.J. & Ploberger, W. (1997) Asymptotic theory of integrated conditional moment tests. Econometrica 65, 1129–1151.CrossRefGoogle Scholar
Billingsley, P. (1968) Convergence of Probability Measures. Wiley.Google Scholar
Boning, B. & Sowell, F. (1999) Optimality of the integrated conditional moment test. Econometric Theory 15, 710–719.CrossRefGoogle Scholar
Cameron, A.C. & Trivedi, P.K. (1986) Econometric models based on count data: Comparisons and applications of some estimators and tests. Journal of Applied Econometrics 1, 29–53.CrossRefGoogle Scholar
Cameron, A.C. & Trivedi, P.K. (1990) Regression-based tests for overdispersion in the Poisson model. Journal of Econometrics 46, 347–364.CrossRefGoogle Scholar
Chernick, M. (1999) Bootstrap Methods: A Practitioner’s Guide. Wiley.Google Scholar
Chung, K.L. (1974) A Course in Probability Theory. Academic Press.Google Scholar
Deb, P. & Trivedi, P.K. (1997) Demand for medical care by the elderly. Journal of Applied Econometrics 12, 313–336.3.0.CO;2-G>CrossRefGoogle Scholar
Efron, B. (1979) Bootstrap methods: Another look at the jackknife. Annals of Statistics 7, 1–26.CrossRefGoogle Scholar
Escanciano, J.C. (2006) A consistent diagnostic test for regression models using projections. Econometric Theory 22, 1030–1051.CrossRefGoogle Scholar
Fan, Y.Q. & Li, Q. (2000) Consistent model specification tests: Kernel-based tests versus Bierens’ ICM tests. Econometric Theory 16, 1016–1041.CrossRefGoogle Scholar
Gozalo, P.L. (1993) A consistent model specification test for nonparametric estimation of regression function models. Econometric Theory 9, 451– 477.CrossRefGoogle Scholar
Hadinejad-Mahram, H., Dahlhaus, D., & Blomker, D. (2002) Karhunen-Loeve Expansion of Vector Random Processes. Technical Report IKT-NT 1019, Communications Technological Laboratory, Swiss Federal Institute of Technology, Zurich.Google Scholar
Hannan, E.J. & Quinn, B.G. (1979) The determination of the order of an autoregression. Journal of the Royal Statistical Society, Series B 41, 190–195.Google Scholar
Härdle, W. & Mammen, E. (1993) Comparing nonparametric versus parametric regression fits. Annals of Statistics 21, 1926–1947.CrossRefGoogle Scholar
Hong, Y. & White, H. (1995) Consistent specification testing via nonparametric series regression. Econometrica 63, 1133–1159.CrossRefGoogle Scholar
Horowitz, J.T. & Härdle, W. (1994) Testing a parametric model against a semiparametric alternative. Econometric Theory 10, 821–848.CrossRefGoogle Scholar
Jennrich, R.I. (1969) Asymptotic properties of non-linear least squares estimators. Annals of Mathematical Statistics 40, 633–643.CrossRefGoogle Scholar
Krein, M.G. (1998) Compact linear operators on functional spaces with two norms. Integral Equations and Operator Theory 30, 140–162.CrossRefGoogle Scholar
Kullback, L. & Leibler, R.A. (1951) On information and sufficiency. Annals of Mathematical Statistics 22, 79–86.CrossRefGoogle Scholar
Lavergne, P. & Vuong, Q.H. (2000) A nonparametric significance test. Econometric Theory 16, 576–601.CrossRefGoogle Scholar
Lee, L.F. (1986) Specification test for Poisson regression models. International Economic Review 27, 689–706.CrossRefGoogle Scholar
Li, F. & Tkacz, G. (1996) A consistent bootstrap test for conditional density functions with time-series data. Journal of Econometrics 133, 863–886.CrossRefGoogle Scholar
Li, Q. & Wang, S. (1998) A simple consistent bootstrap test for a parametric regression function. Journal of Econometrics 87, 145–165.CrossRefGoogle Scholar
McLeish, D.L. (1974) Dependent central limit theorems and invariance principles. Annals of Probability 2, 620–628.CrossRefGoogle Scholar
Schwarz, G. (1978) Estimating the dimension of a model. Annals of Statistics 6, 461–464.CrossRefGoogle Scholar
Stinchcombe, M. & White, H. (1998) Consistent specification testing with nuisance parameters present only under the alternative. Econometric Theory 14, 295–325.CrossRefGoogle Scholar
Stute, W. (1997) Nonparametric model checks for regression. Annals of Statistics 25, 613–641.CrossRefGoogle Scholar
White, H. (1982) Maximum likelihood estimation of misspecified models. Econometrica 50, 1–25.CrossRefGoogle Scholar
White, H. (1994) Estimation, Inference and Specification Analysis. Cambridge University Press.CrossRefGoogle Scholar
Zheng, J.X. (1996) A consistent test of functional form via nonparametric estimation techniques. Journal of Econometrics 75, 263–289.CrossRefGoogle Scholar
Zheng, J.X. (2000) A consistent test of conditional parametric distributions. Econometric Theory 16, 667–691.CrossRefGoogle Scholar