IDEAS home Printed from https://ideas.repec.org/a/spr/metrik/v86y2023i1d10.1007_s00184-022-00861-6.html
   My bibliography  Save this article

An analog of Bickel–Rosenblatt test for fitting an error density in the two phase linear regression model

Author

Listed:
  • Fuxia Cheng

    (Illinois State University)

  • Hira L. Koul

    (Michigan State University)

Abstract

This paper discusses a test of goodness-of-fit of a known error density in a two phase linear regression model in the case jump size at the phase transition point is fixed or tends to zero with the increasing sample size. The proposed test is based on an integrated square difference between a nonparametric error density estimator obtained from the residuals and its expected value under the null error density when the underlying regression parameters are known. The paper establishes the asymptotic normality of the proposed test statistic under the null hypothesis and under certain global $$L_2$$ L 2 alternatives. The asymptotic null distribution of the test statistic is the same as in the case of the known regression parameters. Under the chosen alternatives, unlike in the linear autoregressive time series models with known intercept, it depends on the parameters and their estimates in general. We also describe the analogous results for the self-exciting threshold autoregressive time series model of order 1.

Suggested Citation

  • Fuxia Cheng & Hira L. Koul, 2023. "An analog of Bickel–Rosenblatt test for fitting an error density in the two phase linear regression model," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 86(1), pages 27-56, January.
    • Handle: RePEc:spr:metrik:v:86:y:2023:i:1:d:10.1007_s00184-022-00861-6
    DOI: 10.1007/s00184-022-00861-6
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s00184-022-00861-6
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.
    File URL: https://libkey.io/10.1007/s00184-022-00861-6?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    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. Bachmann, Dirk & Dette, Holger, 2005. "A note on the Bickel-Rosenblatt test in autoregressive time series," Statistics & Probability Letters, Elsevier, vol. 74(3), pages 221-234, October.
    2. Bruce E. Hansen, 2000. "Sample Splitting and Threshold Estimation," Econometrica, Econometric Society, vol. 68(3), pages 575-604, May.
    3. Hira Koul & Nao Mimoto, 2012. "A goodness-of-fit test for GARCH innovation density," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 75(1), pages 127-149, January.
    4. Koul, Hira L. & Qian, Lianfen & Surgailis, Donatas, 2003. "Asymptotics of M-estimators in two-phase linear regression models," Stochastic Processes and their Applications, Elsevier, vol. 103(1), pages 123-154, January.
    5. 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.
    6. Cheng, Fuxia & Sun, Shuxia, 2008. "A goodness-of-fit test of the errors in nonlinear autoregressive time series models," Statistics & Probability Letters, Elsevier, vol. 78(1), pages 50-59, January.
    Full references (including those not matched with items on IDEAS)

    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. Yu, Ping & Phillips, Peter C.B., 2018. "Threshold regression with endogeneity," Journal of Econometrics, Elsevier, vol. 203(1), pages 50-68.
    2. Gao, Min & Yang, Wenzhi & Wu, Shipeng & Yu, Wei, 2022. "Asymptotic normality of residual density estimator in stationary and explosive autoregressive models," Computational Statistics & Data Analysis, Elsevier, vol. 175(C).
    3. Yan-Yu Chiou & Mei-Yuan Chen & Jau-er Chen, 2017. "Nonparametric Regression with Multiple Thresholds: Estimation and Inference," Papers 1705.09418, arXiv.org, revised Feb 2018.
    4. Yury Kutoyants, 2012. "On identification of the threshold diffusion processes," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 64(2), pages 383-413, April.
    5. Chiou, Yan-Yu & Chen, Mei-Yuan & Chen, Jau-er, 2018. "Nonparametric regression with multiple thresholds: Estimation and inference," Journal of Econometrics, Elsevier, vol. 206(2), pages 472-514.
    6. Chiu, Chien-Liang & Chang, Ting-Huan, 2009. "What proportion of renewable energy supplies is needed to initially mitigate CO2 emissions in OECD member countries?," Renewable and Sustainable Energy Reviews, Elsevier, vol. 13(6-7), pages 1669-1674, August.
    7. Bosker, Maarten & Brakman, Steven & Garretsen, Harry & Schramm, Marc, 2008. "A century of shocks: The evolution of the German city size distribution 1925-1999," Regional Science and Urban Economics, Elsevier, vol. 38(4), pages 330-347, July.
    8. Simplice A. Asongu & Nicholas M. Odhiambo, 2020. "Insurance Policy Thresholds for Economic Growth in Africa," The European Journal of Development Research, Palgrave Macmillan;European Association of Development Research and Training Institutes (EADI), vol. 32(3), pages 672-689, July.
    9. Marcelo Fernandes & Breno Neri, 2010. "Nonparametric Entropy-Based Tests of Independence Between Stochastic Processes," Econometric Reviews, Taylor & Francis Journals, vol. 29(3), pages 276-306.
    10. Patrick Zschech & Kai Heinrich & Raphael Bink & Janis S. Neufeld, 2019. "Prognostic Model Development with Missing Labels," Business & Information Systems Engineering: The International Journal of WIRTSCHAFTSINFORMATIK, Springer;Gesellschaft für Informatik e.V. (GI), vol. 61(3), pages 327-343, June.
    11. Dominique Guegan & Florian Ielpo, 2007. "Further evidence on the impact of economic news on interest rates," Post-Print halshs-00188331, HAL.
    12. Murase, Koichi, 2013. "Asymmetric effects of the exchange rate on domestic corporate goods prices," Japan and the World Economy, Elsevier, vol. 25, pages 80-89.
    13. Zheng, Yingmei & Qi, Jianhong & Chen, Xiaoliang, 2011. "The effect of increasing exports on industrial energy intensity in China," Energy Policy, Elsevier, vol. 39(5), pages 2688-2698, May.
    14. Francisco Javier Forcadell & Fernando Úbeda, 2022. "Individual entrepreneurial orientation and performance: the mediating role of international entrepreneurship," International Entrepreneurship and Management Journal, Springer, vol. 18(2), pages 875-900, June.
    15. Pitarakis Jean-Yves, 2006. "Model Selection Uncertainty and Detection of Threshold Effects," Studies in Nonlinear Dynamics & Econometrics, De Gruyter, vol. 10(1), pages 1-30, March.
    16. Kelbesa Megersa & Danny Cassimon, 2015. "Public Debt, Economic Growth, and Public Sector Management in Developing Countries: Is There a Link?," Public Administration & Development, Blackwell Publishing, vol. 35(5), pages 329-346, December.
    17. Fawaz, Fadi & Rahnamamoghadam, Masha & Valcarcel, Victor, 2014. "A Refinement of the Relationship between Economic Growth and Income Inequality in Developing Countries," MPRA Paper 55268, University Library of Munich, Germany.
    18. Young-Joo Kim & Myung Hwan Seo, 2017. "Is There a Jump in the Transition?," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 35(2), pages 241-249, April.
    19. Jess Benhabib & Mark M. Spiegel, 2009. "Moderate Inflation and the Deflation-Depression Link," Journal of Money, Credit and Banking, Blackwell Publishing, vol. 41(4), pages 787-798, June.
    20. Sylwester Bejger, 2019. "Wholesale fuel price adjustment in Poland: examination of competi-tive performance," Ekonomia i Prawo, Uniwersytet Mikolaja Kopernika, vol. 18(4), pages 385-412, December.

    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:spr:metrik:v:86:y:2023:i:1:d:10.1007_s00184-022-00861-6. 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: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    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.