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Model Specification Tests in Nonparametric Stochastic Regression Models

  • Gao, Jiti
  • Tong, Howell
  • Wolff, Rodney

In this paper, we consider testing for additivity in a class of nonparametric stochastic regression models. Two test statistics are constructed and their asymptotic distributions are established. We also conduct a small sample study for one of the test statistics through a simulated example.

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Article provided by Elsevier in its journal Journal of Multivariate Analysis.

Volume (Year): 83 (2002)
Issue (Month): 2 (November)
Pages: 324-359

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Handle: RePEc:eee:jmvana:v:83:y:2002:i:2:p:324-359
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  1. Rodney C Wolff & Jiti Gao & Howell Tong, 2006. "Adaptive orthogonal series estimation in additive stochastic regression models," School of Economics and Finance Discussion Papers and Working Papers Series 208k, School of Economics and Finance, Queensland University of Technology.
  2. Eubank, R. L. & Kambour, E. L. & Kim, J. T. & Klipple, K. & Reese, C. S. & Schimek, M., 1998. "Estimation in partially linear models," Computational Statistics & Data Analysis, Elsevier, vol. 29(1), pages 27-34, November.
  3. Eastwood, Brian J. & Gallant, A. Ronald, 1991. "Adaptive Rules for Seminonparametric Estimators That Achieve Asymptotic Normality," Econometric Theory, Cambridge University Press, vol. 7(03), pages 307-340, September.
  4. Li, Qi, 1999. "Consistent model specification tests for time series econometric models," Journal of Econometrics, Elsevier, vol. 92(1), pages 101-147, September.
  5. Cox, Dennis D. & Kim, Tae Yoon, 1995. "Moment bounds for mixing random variables useful in nonparametric function estimation," Stochastic Processes and their Applications, Elsevier, vol. 56(1), pages 151-158, March.
  6. Gallant, A. Ronald, 1981. "On the bias in flexible functional forms and an essentially unbiased form : The fourier flexible form," Journal of Econometrics, Elsevier, vol. 15(2), pages 211-245, February.
  7. Hardle, W. & Kneip, A., 1998. "Testing a Regression Model when we Have Smooth Alternatives in Mind," Papers 9808, Catholique de Louvain - Institut de statistique.
  8. Vidar Hjellvik & Qiwei Yao & Dag Tjostheim, 1998. "Linearity testing using local polynominal approximation," LSE Research Online Documents on Economics 6638, London School of Economics and Political Science, LSE Library.
  9. Donald W.K. Andrews, 1988. "Asymptotic Normality of Series Estimators for Nonparametric and Semiparametric Regression Models," Cowles Foundation Discussion Papers 874R, Cowles Foundation for Research in Economics, Yale University, revised May 1989.
  10. Hall, Peter, 1984. "Central limit theorem for integrated square error of multivariate nonparametric density estimators," Journal of Multivariate Analysis, Elsevier, vol. 14(1), pages 1-16, February.
  11. Lavergne, Pascal & Vuong, Quang, 2000. "Nonparametric Significance Testing," Econometric Theory, Cambridge University Press, vol. 16(04), pages 576-601, August.
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  13. 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.
  14. Hong, Yongmiao & White, Halbert, 1995. "Consistent Specification Testing via Nonparametric Series Regression," Econometrica, Econometric Society, vol. 63(5), pages 1133-59, September.
  15. Masry, Elias & Tjøstheim, Dag, 1995. "Nonparametric Estimation and Identification of Nonlinear ARCH Time Series Strong Convergence and Asymptotic Normality: Strong Convergence and Asymptotic Normality," Econometric Theory, Cambridge University Press, vol. 11(02), pages 258-289, February.
  16. Fan, Yanqin & Li, Qi, 1996. "Consistent Model Specification Tests: Omitted Variables and Semiparametric Functional Forms," Econometrica, Econometric Society, vol. 64(4), pages 865-90, July.
  17. Masry, Elias & Tjøstheim, Dag, 1997. "Additive Nonlinear ARX Time Series and Projection Estimates," Econometric Theory, Cambridge University Press, vol. 13(02), pages 214-252, April.
  18. Jianqing Fan & Qiwei Yao, 1998. "Efficient estimation of conditional variance functions in stochastic regression," LSE Research Online Documents on Economics 6635, London School of Economics and Political Science, LSE Library.
  19. Boente, Graciela & Fraiman, Ricardo, 1988. "Consistency of a nonparametric estimate of a density function for dependent variables," Journal of Multivariate Analysis, Elsevier, vol. 25(1), pages 90-99, April.
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