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Model Specification Tests in Nonparametric Stochastic Regression Models

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

Abstract

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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Bibliographic Info

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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Related research

Keywords: additivity dependent process model determination nonlinear time series nonparametric regression semiparametric autoregression;

References

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  1. 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.
  2. 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.
  3. Li, Qi, 1999. "Consistent model specification tests for time series econometric models," Journal of Econometrics, Elsevier, vol. 92(1), pages 101-147, September.
  4. 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.
  5. repec:wop:humbsf:2000-21 is not listed on IDEAS
  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.
  7. Haerdle,Wolfgang & Kneip,Alois, 1992. "Testing aregression model when we have smooth alternatives in mind," Discussion Paper Serie A 389, University of Bonn, Germany.
  8. 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.
  9. 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.
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  11. 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.
  12. 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.
  13. 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.
  14. 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.
  15. 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.
  16. Hong, Yongmiao & White, Halbert, 1995. "Consistent Specification Testing via Nonparametric Series Regression," Econometrica, Econometric Society, vol. 63(5), pages 1133-59, September.
  17. Lavergne, Pascal & Vuong, Quang, 1998. "Nonparametric significance testing," SFB 373 Discussion Papers 1998,75, Humboldt University of Berlin, Interdisciplinary Research Project 373: Quantification and Simulation of Economic Processes.
  18. 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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  20. 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.
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Citations

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Cited by:
  1. Song Xi Chen & Jiti Gao, 2010. "Simultaneous Testing of Mean and Variance Structures in Nonlinear Time Series Models," School of Economics Working Papers 2010-28, University of Adelaide, School of Economics.
  2. repec:wyi:journl:002062 is not listed on IDEAS
  3. Chaohua Dong & Jiti Gao, 2014. "Specification Testing in Structural Nonparametric Cointegration," Monash Econometrics and Business Statistics Working Papers 2/14, Monash University, Department of Econometrics and Business Statistics.
  4. Gao, Jiti & Tong, Howell, 2002. "Nonparametric and semiparametric regression model selection," MPRA Paper 11987, University Library of Munich, Germany, revised Feb 2004.
  5. Sophie DABO-NIANG & Christian FRANCQ & Jean-Michel ZAKOIAN, 2009. "Combining Nonparametric and Optimal Linear Time Series Predictions," Working Papers 2009-18, Centre de Recherche en Economie et Statistique.
  6. Chaohua Dong & Jiti Gao, 2012. "Specification Testing Driven by Orthogonal Series in Nonstationary Time Series Models," Monash Econometrics and Business Statistics Working Papers 20/12, Monash University, Department of Econometrics and Business Statistics.
  7. 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.
  8. Gao, Jiti, 2007. "Nonlinear time series: semiparametric and nonparametric methods," MPRA Paper 39563, University Library of Munich, Germany, revised 01 Sep 2007.
  9. Chen, Song Xi & Gao, Jiti, 2007. "An adaptive empirical likelihood test for parametric time series regression models," Journal of Econometrics, Elsevier, vol. 141(2), pages 950-972, December.
  10. Bin Peng & Chaohua Dong & Jiti Gao, 2014. "Semiparametric Single-Index Panel Data Models with Cross-Sectional Dependence," Monash Econometrics and Business Statistics Working Papers 9/14, Monash University, Department of Econometrics and Business Statistics.
  11. Chaohua Dong & Jiti Gao & Dag Tjostheim, 2014. "Estimation for Single-index and Partially Linear Single-index Nonstationary Time Series Models," Monash Econometrics and Business Statistics Working Papers 7/14, Monash University, Department of Econometrics and Business Statistics.
  12. Dabo-Niang, Sophie & Francq, Christian & Zakoian, Jean-Michel, 2009. "Combining parametric and nonparametric approaches for more efficient time series prediction," MPRA Paper 16893, University Library of Munich, Germany.

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