IDEAS home Printed from https://ideas.repec.org/a/eee/jmvana/v83y2002i2p324-359.html
   My bibliography  Save this article

Model Specification Tests in Nonparametric Stochastic Regression Models

Author

Listed:
  • 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.

Suggested Citation

  • Gao, Jiti & Tong, Howell & Wolff, Rodney, 2002. "Model Specification Tests in Nonparametric Stochastic Regression Models," Journal of Multivariate Analysis, Elsevier, vol. 83(2), pages 324-359, November.
  • Handle: RePEc:eee:jmvana:v:83:y:2002:i:2:p:324-359
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0047-259X(01)92058-5
    Download Restriction: Full text for ScienceDirect subscribers only
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Masry, Elias & Tjøstheim, Dag, 1997. "Additive Nonlinear ARX Time Series and Projection Estimates," Econometric Theory, Cambridge University Press, vol. 13(2), pages 214-252, April.
    2. Hardle, Wolfgang & LIang, Hua & Gao, Jiti, 2000. "Partially linear models," MPRA Paper 39562, University Library of Munich, Germany, revised 01 Sep 2000.
    3. Robinson, Peter M, 1988. "Root- N-Consistent Semiparametric Regression," Econometrica, Econometric Society, vol. 56(4), pages 931-954, July.
    4. Andrews, Donald W K, 1991. "Asymptotic Normality of Series Estimators for Nonparametric and Semiparametric Regression Models," Econometrica, Econometric Society, vol. 59(2), pages 307-345, March.
    5. Li, Qi, 1999. "Consistent model specification tests for time series econometric models," Journal of Econometrics, Elsevier, vol. 92(1), pages 101-147, September.
    6. Wolfgang Härdle & Philippe Vieu, 1992. "Kernel Regression Smoothing Of Time Series," Journal of Time Series Analysis, Wiley Blackwell, vol. 13(3), pages 209-232, May.
    7. 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.
    8. Lavergne, Pascal & Vuong, Quang, 2000. "Nonparametric Significance Testing," Econometric Theory, Cambridge University Press, vol. 16(4), pages 576-601, August.
    9. Hjellvik, Vidar & Yao, Qiwei & Tjostheim, Dag, 1998. "Linearity testing using local polynominal approximation," LSE Research Online Documents on Economics 6638, London School of Economics and Political Science, LSE Library.
    10. Fan J. & Huang L-S., 2001. "Goodness-of-Fit Tests for Parametric Regression Models," Journal of the American Statistical Association, American Statistical Association, vol. 96, pages 640-652, June.
    11. Fan, Yanqin & Li, Qi, 1996. "Consistent Model Specification Tests: Omitted Variables and Semiparametric Functional Forms," Econometrica, Econometric Society, vol. 64(4), pages 865-890, July.
    12. J. Bowers & B. Brown & J. Springer & L. Tollefson & R. Lorentzen & S. Henry, 1993. "Risk Assessment for Aflatoxin: An Evaluation Based on the Multistage Model," Risk Analysis, John Wiley & Sons, vol. 13(6), pages 637-642, December.
    13. Jiti Gao & Hua Liang, 1997. "Statistical Inference in Single-Index and Partially Nonlinear Models," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 49(3), pages 493-517, September.
    14. Wolfgang Härdle & Alois Kneip, 1999. "Testing a Regression Model When We Have Smooth Alternatives in Mind," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 26(2), pages 221-238, June.
    15. Eastwood, Brian J. & Gallant, A. Ronald, 1991. "Adaptive Rules for Seminonparametric Estimators That Achieve Asymptotic Normality," Econometric Theory, Cambridge University Press, vol. 7(3), pages 307-340, September.
    16. Hong, Yongmiao & White, Halbert, 1995. "Consistent Specification Testing via Nonparametric Series Regression," Econometrica, Econometric Society, vol. 63(5), pages 1133-1159, September.
    17. Fan, Jianqing & Yao, Qiwei, 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.
    18. Chi‐ming Wong & Robert Kohn, 1996. "A Bayesian Approach To Estimating And Forecasting Additive Nonparametric Autoregressive Models," Journal of Time Series Analysis, Wiley Blackwell, vol. 17(2), pages 203-220, March.
    19. 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.
    20. 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.
    21. 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.
    22. 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(2), pages 258-289, February.
    23. 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.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. 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.
    2. Pourkhanali, Armin & Tafakori, Laleh & Bee, Marco, 2023. "Forecasting Value-at-Risk using functional volatility incorporating an exogenous effect," International Review of Financial Analysis, Elsevier, vol. 89(C).
    3. 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.
    4. Dabo-Niang, Sophie & Francq, Christian & Zakoïan, Jean-Michel, 2010. "Combining Nonparametric and Optimal Linear Time Series Predictions," Journal of the American Statistical Association, American Statistical Association, vol. 105(492), pages 1554-1565.
    5. Weilun Zhou & Jiti Gao & David Harris & Hsein Kew, 2019. "Semiparametric Single-index Predictive Regression," Monash Econometrics and Business Statistics Working Papers 25/19, Monash University, Department of Econometrics and Business Statistics.
    6. Gao, Jiti & Tong, Howell, 2002. "Nonparametric and semiparametric regression model selection," MPRA Paper 11987, University Library of Munich, Germany, revised Feb 2004.
    7. Dong, Chaohua & Gao, Jiti & Peng, Bin, 2015. "Semiparametric single-index panel data models with cross-sectional dependence," Journal of Econometrics, Elsevier, vol. 188(1), pages 301-312.
    8. repec:wyi:journl:002062 is not listed on IDEAS
    9. Lin, Yingqian & Tu, Yundong, 2020. "Sieve extremum estimation of a semiparametric transformation model," Economics Letters, Elsevier, vol. 189(C).
    10. Gao, Jiti, 2007. "Nonlinear time series: semiparametric and nonparametric methods," MPRA Paper 39563, University Library of Munich, Germany, revised 01 Sep 2007.
    11. Song Xi Chen & Jiti Gao, 2010. "Simultaneous Testing of Mean and Variance Structures in Nonlinear Time Series Models," School of Economics and Public Policy Working Papers 2010-28, University of Adelaide, School of Economics and Public Policy.
    12. 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.
    13. Ivan Korolev, 2018. "A Consistent Heteroskedasticity Robust LM Type Specification Test for Semiparametric Models," Papers 1810.07620, arXiv.org, revised Nov 2019.
    14. 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.
    15. Feng, Guohua & Peng, Bin & Su, Liangjun & Yang, Thomas Tao, 2019. "Semi-parametric single-index panel data models with interactive fixed effects: Theory and practice," Journal of Econometrics, Elsevier, vol. 212(2), pages 607-622.
    16. Zhou, Weilun & Gao, Jiti & Harris, David & Kew, Hsein, 2024. "Semi-parametric single-index predictive regression models with cointegrated regressors," Journal of Econometrics, Elsevier, vol. 238(1).
    17. 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.
    18. Dong, Chaohua & Linton, Oliver & Peng, Bin, 2021. "A weighted sieve estimator for nonparametric time series models with nonstationary variables," Journal of Econometrics, Elsevier, vol. 222(2), pages 909-932.
    19. 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.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Gao, Jiti, 2007. "Nonlinear time series: semiparametric and nonparametric methods," MPRA Paper 39563, University Library of Munich, Germany, revised 01 Sep 2007.
    2. Hardle, Wolfgang & LIang, Hua & Gao, Jiti, 2000. "Partially linear models," MPRA Paper 39562, University Library of Munich, Germany, revised 01 Sep 2000.
    3. Qi Li & Jeffrey Scott Racine, 2006. "Nonparametric Econometrics: Theory and Practice," Economics Books, Princeton University Press, edition 1, volume 1, number 8355.
    4. 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.
    5. Shengfang Tang & Zongwu Cai & Ying Fang & Ming Lin, 2019. "Testing Unconfoundedness Assumption Using Auxiliary Variables," WORKING PAPERS SERIES IN THEORETICAL AND APPLIED ECONOMICS 201905, University of Kansas, Department of Economics, revised Mar 2019.
    6. Gao, Jiti & Anh, Vo, 2000. "A central limit theorem for a random quadratic form of strictly stationary processes," Statistics & Probability Letters, Elsevier, vol. 49(1), pages 69-79, August.
    7. Ait-Sahalia, Yacine & Bickel, Peter J. & Stoker, Thomas M., 2001. "Goodness-of-fit tests for kernel regression with an application to option implied volatilities," Journal of Econometrics, Elsevier, vol. 105(2), pages 363-412, December.
    8. Zongwu Cai & Ying Fang & Ming Lin & Shengfang Tang, 2020. "Testing Unconfoundedness Assumption Using Auxiliary Variables," WORKING PAPERS SERIES IN THEORETICAL AND APPLIED ECONOMICS 202004, University of Kansas, Department of Economics, revised Feb 2020.
    9. Gao, Jiti & Tong, Howell, 2002. "Nonparametric and semiparametric regression model selection," MPRA Paper 11987, University Library of Munich, Germany, revised Feb 2004.
    10. Lavergne, Pascal, 2001. "An equality test across nonparametric regressions," Journal of Econometrics, Elsevier, vol. 103(1-2), pages 307-344, July.
    11. Masamune Iwasawa, 2015. "A Joint Specification Test for Response Probabilities in Unordered Multinomial Choice Models," Econometrics, MDPI, vol. 3(3), pages 1-31, September.
    12. Gupta, A, 2015. "Nonparametric specification testing via the trinity of tests," Economics Discussion Papers 15619, University of Essex, Department of Economics.
    13. Gupta, Abhimanyu, 2018. "Nonparametric specification testing via the trinity of tests," Journal of Econometrics, Elsevier, vol. 203(1), pages 169-185.
    14. Ying Fang & Ming Lin & Shengfang Tang & Zongwu Cai, 2021. "Testing Conditional Independence in Macroeconomic Policy Evaluation for Time Series Data," WORKING PAPERS SERIES IN THEORETICAL AND APPLIED ECONOMICS 202118, University of Kansas, Department of Economics, revised Sep 2021.
    15. repec:esx:essedp:774 is not listed on IDEAS
    16. Patrick Saart & Jiti Gao & Nam Hyun Kim, 2014. "Semiparametric methods in nonlinear time series analysis: a selective review," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 26(1), pages 141-169, March.
    17. Li, Qi & Hsiao, Cheng & Zinn, Joel, 2003. "Consistent specification tests for semiparametric/nonparametric models based on series estimation methods," Journal of Econometrics, Elsevier, vol. 112(2), pages 295-325, February.
    18. Su, Liangjun & White, Halbert, 2007. "A consistent characteristic function-based test for conditional independence," Journal of Econometrics, Elsevier, vol. 141(2), pages 807-834, December.
    19. Fang, Ying & Tang, Shengfang & Cai, Zongwu & Lin, Ming, 2020. "An alternative test for conditional unconfoundedness using auxiliary variables," Economics Letters, Elsevier, vol. 194(C).
    20. Gao, Jiti & Hong, Yongmiao, 2007. "Central limit theorems for weighted quadratic forms of dependent processes with applications in specification testing," MPRA Paper 11977, University Library of Munich, Germany, revised Dec 2007.
    21. Lin, Zhongjian & Li, Qi & Sun, Yiguo, 2014. "A consistent nonparametric test of parametric regression functional form in fixed effects panel data models," Journal of Econometrics, Elsevier, vol. 178(P1), pages 167-179.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:jmvana:v:83:y:2002:i:2:p:324-359. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/wps/find/journaldescription.cws_home/622892/description#description .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.