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Tests of Specification for Parametric and Semiparametric Models

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Author Info
Yoon-Jae Whang
Donald W.K. Andrews () (Cowles Foundation, Yale University)

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Abstract

This paper provides a general framework for constructing specification tests for parametric and semiparametric models. The paper develops new specification tests using the general framework. In particular, specification tests for semiparametric partially linear regression, sample selection, and censored regression models are introduced. The results apply in time series and cross-sectional contexts. The method of proof exploits results concerning the stochastic equicontinuity or weak convergence of normalized sums of stochastic processes.

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Publisher Info
Paper provided by Cowles Foundation, Yale University in its series Cowles Foundation Discussion Papers with number 968.

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Length: 80 pages
Date of creation: Jan 1991
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Publication status: Published in Journal of Econometrics (1993), 57: 277-318
Handle: RePEc:cwl:cwldpp:968

Note: CFP 844.
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Postal: Yale University, Box 208281, New Haven, CT 06520-8281 USA
Phone: (203) 432-3702
Fax: (203) 432-6167
Web page: http://cowles.econ.yale.edu/
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Postal: Cowles Foundation, Yale University, Box 208281, New Haven, CT 06520-8281 USA

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Related research
Keywords: Infinite dimensional nuisance parameter; semiparametric model; specification test; stochastic equicontinuity;

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References listed on IDEAS
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
  1. Newey, Whitney K & West, Kenneth D, 1987. "A Simple, Positive Semi-definite, Heteroskedasticity and Autocorrelation Consistent Covariance Matrix," Econometrica, Econometric Society, vol. 55(3), pages 703-08, May. [Downloadable!] (restricted)
    Other versions:
  2. Potscher, Benedikt M & Prucha, Ingmar R, 1989. "A Uniform Law of Large Numbers for Dependent and Heterogeneous Data Processes," Econometrica, Econometric Society, vol. 57(3), pages 675-83, May. [Downloadable!] (restricted)
    Other versions:
  3. Tauchen, George, 1985. "Diagnostic testing and evaluation of maximum likelihood models," Journal of Econometrics, Elsevier, vol. 30(1-2), pages 415-443. [Downloadable!] (restricted)
  4. Andrews, Donald W K, 1991. "Heteroskedasticity and Autocorrelation Consistent Covariance Matrix Estimation," Econometrica, Econometric Society, vol. 59(3), pages 817-58, May. [Downloadable!] (restricted)
    Other versions:
  5. Whang, Yoon-Jae & Andrews, Donald W. K., 1993. "Tests of specification for parametric and semiparametric models," Journal of Econometrics, Elsevier, vol. 57(1-3), pages 277-318. [Downloadable!] (restricted)
    Other versions:
  6. Amemiya, Takeshi, 1973. "Regression Analysis when the Dependent Variable is Truncated Normal," Econometrica, Econometric Society, vol. 41(6), pages 997-1016, November. [Downloadable!] (restricted)
  7. K. Newey, Whitney, 1985. "Generalized method of moments specification testing," Journal of Econometrics, Elsevier, vol. 29(3), pages 229-256, September. [Downloadable!] (restricted)
  8. Donald W.K. Andrews, 1989. "Asymptotics for Semiparametric Econometric Models: I. Estimation," Cowles Foundation Discussion Papers 908R, Cowles Foundation, Yale University, revised Aug 1990. [Downloadable!]
  9. Robinson, Peter M, 1988. "Root- N-Consistent Semiparametric Regression," Econometrica, Econometric Society, vol. 56(4), pages 931-54, July. [Downloadable!] (restricted)
  10. A. R. Pagan & A. D. Hall, 1983. "Diagnostic tests as residual analysis," Econometric Reviews, Taylor and Francis Journals, vol. 2(2), pages 159-218. [Downloadable!] (restricted)
  11. Andrews, Donald W. K., 1987. "Laws of Large Numbers for Dependent Non-Identically Distributed Random Variables," Working Papers 645, California Institute of Technology, Division of the Humanities and Social Sciences. [Downloadable!]
  12. Andrews, Donald W K, 1991. "Asymptotic Normality of Series Estimators for Nonparametric and Semiparametric Regression Models," Econometrica, Econometric Society, vol. 59(2), pages 307-45, March. [Downloadable!] (restricted)
    Other versions:
  13. Koenker, Roger, 1981. "A note on studentizing a test for heteroscedasticity," Journal of Econometrics, Elsevier, vol. 17(1), pages 107-112, September. [Downloadable!] (restricted)
  14. Newey, W.K., 1989. "Uniform Convergence In Probability And Stochastic Equicontinuity," Papers 342, Princeton, Department of Economics - Econometric Research Program.
  15. Hausman, Jerry A, 1978. "Specification Tests in Econometrics," Econometrica, Econometric Society, vol. 46(6), pages 1251-71, November. [Downloadable!] (restricted)
  16. Donald W.K. Andrews, 1989. "Asymptotics for Semiparametric Econometric Models: II. Stochastic Equicontinuity and Nonparametric Kernel Estimation," Cowles Foundation Discussion Papers 909R, Cowles Foundation, Yale University, revised Jul 1990. [Downloadable!]
  17. Breusch, T S & Pagan, A R, 1979. "A Simple Test for Heteroscedasticity and Random Coefficient Variation," Econometrica, Econometric Society, vol. 47(5), pages 1287-94, September. [Downloadable!] (restricted)
  18. Pagan, Adrian & Vella, Frank, 1989. "Diagnostic Tests for Models Based on Individual Data: A Survey," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 4(S), pages S29-59, Supplemen. [Downloadable!] (restricted)
  19. Newey, Whitney K, 1985. "Maximum Likelihood Specification Testing and Conditional Moment Tests," Econometrica, Econometric Society, vol. 53(5), pages 1047-70, September. [Downloadable!] (restricted)
  20. Donald W.K. Andrews, 1986. "Consistency in Nonlinear Econometric Models: A Generic Uniform Law of Large Numbers," Cowles Foundation Discussion Papers 790, Cowles Foundation, Yale University. [Downloadable!]
  21. Arabmazar, Abbas & Schmidt, Peter, 1982. "An Investigation of the Robustness of the Tobit Estimator to Non-Normality," Econometrica, Econometric Society, vol. 50(4), pages 1055-63, July. [Downloadable!] (restricted)
  22. White, Halbert, 1982. "Maximum Likelihood Estimation of Misspecified Models," Econometrica, Econometric Society, vol. 50(1), pages 1-25, January. [Downloadable!] (restricted)
  23. Powell, James L., 1984. "Least absolute deviations estimation for the censored regression model," Journal of Econometrics, Elsevier, vol. 25(3), pages 303-325, July. [Downloadable!] (restricted)
Full references

Cited by:
(explanations, Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.)

  1. Gao, Jiti & King, Maxwell, 2003. "Estimation and model specification testing in nonparametric and semiparametric econometric models," MPRA Paper 11989, University Library of Munich, Germany, revised Feb 2006. [Downloadable!]
  2. Andrew M. Jones & José M. Labeaga, 2003. "Individual heterogeneity and censoring in panel data estimates of tobacco expenditure," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 18(2), pages 157-177. [Downloadable!]
  3. Javier Hidalgo, 1999. "Nonparametric tests for model selection with time series data," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer, vol. 8(2), pages 365-398, December. [Downloadable!] (restricted)
  4. Horowitz, Joel L. & Spokoiny, Vladimir G., 2000. "An Adaptive, Rate-Optimal Test of Linearity for Median Regression Models," Working Papers 00-04, University of Iowa, Department of Economics. [Downloadable!]
  5. Euvals, R. & Melenberg, B. & Soest, A. van, 1997. "Testing the predictive value of subjective labour supply data," Discussion Paper 25, Tilburg University, Center for Economic Research. [Downloadable!]
    Other versions:
  6. Jiti Gao & Hua Liang, 1997. "Statistical Inference in Single-Index and Partially Nonlinear Models," Annals of the Institute of Statistical Mathematics, Springer, vol. 49(3), pages 493-517, September. [Downloadable!] (restricted)
  7. Yoon-Jae Whang, 1993. "A Semiparametric Analysis Of The Life Cycle-Permanent Income Hypothesis," International Economic Journal, Korean International Economic Association, vol. 7(4), pages 89-108, December. [Downloadable!] (restricted)
  8. Aït-Sahalia, Yacine. & Bickel, Peter J. & Stoker, Thomas M., 1994. "Goodness-of-fit tests for regression using kernel methods," Working papers 3747-94., Massachusetts Institute of Technology (MIT), Sloan School of Management. [Downloadable!]
  9. Horowitz, Joel L. & Spokoiny, Vladimir G., 1999. "An Adaptive, Rate-Optimal Test of a Parametric Model Against a Nonparametric Alternative," Working Papers 99-02, University of Iowa, Department of Economics. [Downloadable!]
  10. Gary Gorton & Frank A. Schmid, 1996. "Universal Banking and the Performance of German Firms," NBER Working Papers 5453, National Bureau of Economic Research, Inc. [Downloadable!] (restricted)
  11. Halbert White & Yongmiao Hong, 1999. "M-Testing Using Finite and Infinite Dimensional Parameter Estimators," University of California at San Diego, Economics Working Paper Series 1993-01R, Department of Economics, UC San Diego. [Downloadable!]
    Other versions:
  12. Donald W.K. Andrews, 1992. "An Introduction to Econometric Applications of Functional Limit Theory for Dependent Random Variables," Cowles Foundation Discussion Papers 1020, Cowles Foundation, Yale University. [Downloadable!]
  13. Yoon-Jae Whang & Donald W.K. Andrews, 1991. "Tests of Specification for Parametric and Semiparametric Models," Cowles Foundation Discussion Papers 968, Cowles Foundation, Yale University. [Downloadable!]
    Other versions:
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