IDEAS home Printed from https://ideas.repec.org/a/taf/gnstxx/v23y2011i1p99-114.html

Testing the linearity in partially linear models

Author

Listed:
  • Na Li
  • Xingzhong Xu
  • Pei Jin

Abstract

A test is proposed to check the linearity of the nonparametric portion in the partially linear regression model with a linear interpolation. The test is given by a p-value which is derived using the fiducial method. This p-value can also be thought as a generalised p-value. Under the null hypothesis, the p-value is uniformly distributed on interval (0, 1). Meanwhile the test is consistent under mild conditions. Finally, a good finite sample performance of the test is investigated by simulations, in which comparisons with other tests are also given.

Suggested Citation

  • Na Li & Xingzhong Xu & Pei Jin, 2011. "Testing the linearity in partially linear models," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 23(1), pages 99-114.
    • Handle: RePEc:taf:gnstxx:v:23:y:2011:i:1:p:99-114
    DOI: 10.1080/10485251003615574
    as

    Download full text from publisher

    File URL: http://hdl.handle.net/10.1080/10485251003615574
    Download Restriction: Access to full text is restricted to subscribers.
    File URL: https://libkey.io/10.1080/10485251003615574?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

    for a different version of it.

    References listed on IDEAS

    as
    1. Dennis Cox & Eunmee Koh, 1989. "A smoothing spline based test of model adequacy in polynomial regression," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 41(2), pages 383-400, June.
    2. Richard Blundell & Alan Duncan & Krishna Pendakur, 1998. "Semiparametric estimation and consumer demand," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 13(5), pages 435-461.
    3. Mary C. Meyer, 2003. "A test for linear versus convex regression function using shape-restricted regression," Biometrika, Biometrika Trust, vol. 90(1), pages 223-232, March.
    4. Gerda Claeskens, 2004. "Restricted likelihood ratio lack‐of‐fit tests using mixed spline models," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 66(4), pages 909-926, November.
    5. Gourieroux, Christian & Holly, Alberto & Monfort, Alain, 1982. "Likelihood Ratio Test, Wald Test, and Kuhn-Tucker Test in Linear Models with Inequality Constraints on the Regression Parameters," Econometrica, Econometric Society, vol. 50(1), pages 63-80, January.
    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. Jeremy E. Reynolds, 2014. "Prevailing Preferences," ILR Review, Cornell University, ILR School, vol. 67(3), pages 1017-1041, July.
    2. Wangli Xu & Xu Guo & Lixing Zhu, 2012. "Goodness-of-fitting for partial linear model with missing response at random," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 24(1), pages 103-118.
    3. Wangli Xu & Xu Guo, 2013. "Checking the adequacy of partial linear models with missing covariates at random," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 65(3), pages 473-490, June.
    4. Ravenscroft, Sue & Williams, Paul F., 2021. "Sustaining discreditable accounting research through ignorance: The mainstream elite’s response to the 2008 financial crisis," Accounting, Organizations and Society, Elsevier, vol. 95(C).

    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. Yuichi Kitamura & Jörg Stoye, 2013. "Nonparametric analysis of random utility models: testing," CeMMAP working papers 36/13, Institute for Fiscal Studies.
    2. Martin Carree & Boris Lokshin & René Belderbos, 2011. "A note on testing for complementarity and substitutability in the case of multiple practices," Journal of Productivity Analysis, Springer, vol. 35(3), pages 263-269, June.
    3. Paleti, Rajesh, 2018. "Generalized multinomial probit Model: Accommodating constrained random parameters," Transportation Research Part B: Methodological, Elsevier, vol. 118(C), pages 248-262.
    4. Zand, Fardad & Van Beers, Cees & Van Leeuwen, George, 2011. "Information technology, organizational change and firm productivity: A panel study of complementarity effects and clustering patterns in Manufacturing and Services," MPRA Paper 46469, University Library of Munich, Germany.
    5. Jeffrey M. Wooldridge, 2002. "Inverse probability weighted M-estimators for sample selection, attrition, and stratification," Portuguese Economic Journal, Springer;Instituto Superior de Economia e Gestao, vol. 1(2), pages 117-139, August.
    6. Zaili Fang & Inyoung Kim & Jeesun Jung, 2018. "Semiparametric Kernel-Based Regression for Evaluating Interaction Between Pathway Effect and Covariate," Journal of Agricultural, Biological and Environmental Statistics, Springer;The International Biometric Society;American Statistical Association, vol. 23(1), pages 129-152, March.
    7. Rahul Anand & Naresh Kumar & Mr. Volodymyr Tulin, 2016. "Understanding India’s Food Inflation: The Role of Demand and Supply Factors," IMF Working Papers 2016/002, International Monetary Fund.
    8. Jiang, Feiyu & Li, Dong & Zhu, Ke, 2020. "Non-standard inference for augmented double autoregressive models with null volatility coefficients," Journal of Econometrics, Elsevier, vol. 215(1), pages 165-183.
    9. repec:dau:papers:123456789/13781 is not listed on IDEAS
    10. Marshall, Ben R. & Nguyen, Nhut H. & Visaltanachoti, Nuttawat, 2015. "Frontier market transaction costs and diversification," Journal of Financial Markets, Elsevier, vol. 24(C), pages 1-24.
    11. Mason David M. & Eubank Randy, 2012. "Moderate deviations and intermediate efficiency for lack-of-fit tests," Statistics & Risk Modeling, De Gruyter, vol. 29(2), pages 175-187, June.
    12. Yuichi Kitamura & Jörg Stoye, 2018. "Nonparametric Analysis of Random Utility Models," Econometrica, Econometric Society, vol. 86(6), pages 1883-1909, November.
    13. Isaiah Andrews & Timothy B. Armstrong, 2017. "Unbiased instrumental variables estimation under known first‐stage sign," Quantitative Economics, Econometric Society, vol. 8(2), pages 479-503, July.
    14. Sonja Greven & Ciprian Crainiceanu, 2013. "On likelihood ratio testing for penalized splines," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 97(4), pages 387-402, October.
    15. Hasan Engin Duran & Andrzej Cieślik, 2021. "The distribution of city sizes in Turkey: A failure of Zipf’s law due to concavity," Regional Science Policy & Practice, Wiley Blackwell, vol. 13(5), pages 1702-1719, October.
    16. Hughes, Anthony W. & King, Maxwell L. & Kwek, Kian Teng, 2004. "Selecting the order of an ARCH model," Economics Letters, Elsevier, vol. 83(2), pages 269-275, May.
    17. Blow, Laura & Crawford, Ian, 2002. "A nonparametric method for valuing new goods," Working Paper Series 143, European Central Bank.
    18. Bertrand Candelon & Jan Piplack & Stefan Straetmans, 2009. "Multivariate Business Cycle Synchronization in Small Samples," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 71(5), pages 715-737, October.
    19. Juei-Chao Chen, 1994. "Testing for no effect in nonparametric regression via spline smoothing techniques," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 46(2), pages 251-265, June.
    20. Thanasis Stengos & Yiguo Sun & Dianqin Wang, 2006. "Estimates of semiparametric equivalence scales," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 21(5), pages 629-639, July.
    21. Yulia Kotlyarova & Marcia M Schafgans & Victoria Zinde-Walsh, 2011. "Adapting Kernel Estimation to Uncertain Smoothness," STICERD - Econometrics Paper Series 557, Suntory and Toyota International Centres for Economics and Related Disciplines, LSE.

    More about this item

    Statistics

    Access and download statistics

    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:taf:gnstxx:v:23:y:2011:i:1:p:99-114. 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: Chris Longhurst (email available below). General contact details of provider: http://www.tandfonline.com/GNST20 .

    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.