IDEAS home Printed from https://ideas.repec.org/a/eee/jmvana/v101y2010i4p1026-1041.html

Statistical inference for the index parameter in single-index models

Author

Listed:
  • Zhang, Riquan
  • Huang, Zhensheng
  • Lv, Yazhao

Abstract

In this paper, we are concerned with statistical inference for the index parameter in the single-index model . Based on the estimates obtained by the local linear method, we extend the generalized likelihood ratio test to the single-index model. We investigate the asymptotic behaviour of the proposed test and demonstrate that its limiting null distribution follows a [chi]2-distribution, with the scale constant and the number of degrees of freedom being independent of nuisance parameters or functions, which is called the Wilks phenomenon. A simulated example is used to illustrate the performance of the testing approach.

Suggested Citation

  • Zhang, Riquan & Huang, Zhensheng & Lv, Yazhao, 2010. "Statistical inference for the index parameter in single-index models," Journal of Multivariate Analysis, Elsevier, vol. 101(4), pages 1026-1041, April.
    • Handle: RePEc:eee:jmvana:v:101:y:2010:i:4:p:1026-1041
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0047-259X(09)00167-5
    Download Restriction: Full text for ScienceDirect subscribers only
    ---><---

    As the access to this document is restricted, you may want to

    for a different version of it.

    References listed on IDEAS

    as
    1. Ip, Wai-Cheung & Wong, Heung & Zhang, Riquan, 2007. "Generalized likelihood ratio test for varying-coefficient models with different smoothing variables," Computational Statistics & Data Analysis, Elsevier, vol. 51(9), pages 4543-4561, May.
    2. Jianqing Fan, 2004. "Generalised likelihood ratio tests for spectral density," Biometrika, Biometrika Trust, vol. 91(1), pages 195-209, March.
    3. Hardle, Wolfgang & Tsybakov, A. B., 1993. "How sensitive are average derivatives?," Journal of Econometrics, Elsevier, vol. 58(1-2), pages 31-48, July.
    4. Fan, Jianqing & Jiang, Jiancheng, 2005. "Nonparametric Inferences for Additive Models," Journal of the American Statistical Association, American Statistical Association, vol. 100, pages 890-907, September.
    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. Chaohui Guo & Hu Yang & Jing Lv, 2018. "Two step estimations for a single-index varying-coefficient model with longitudinal data," Statistical Papers, Springer, vol. 59(3), pages 957-983, September.
    2. Huang, Zhensheng & Pang, Zhen & Zhang, Riquan, 2013. "Adaptive profile-empirical-likelihood inferences for generalized single-index models," Computational Statistics & Data Analysis, Elsevier, vol. 62(C), pages 70-82.
    3. Claudio Agostinelli & Ana M. Bianco & Graciela Boente, 2020. "Robust estimation in single-index models when the errors have a unimodal density with unknown nuisance parameter," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 72(3), pages 855-893, June.
    4. Melanie Birke & Sebastien Van Bellegem & Ingrid Van Keilegom, 2017. "Semi-parametric Estimation in a Single-index Model with Endogenous Variables," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 44(1), pages 168-191, March.
    5. Strzalkowska-Kominiak, Ewa & Cao, Ricardo, 2013. "Maximum likelihood estimation for conditional distribution single-index models under censoring," Journal of Multivariate Analysis, Elsevier, vol. 114(C), pages 74-98.
    6. Ewa Strzalkowska-Kominiak & Ricardo Cao, 2014. "Beran-based approach for single-index models under censoring," Computational Statistics, Springer, vol. 29(5), pages 1243-1261, October.

    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. Ip, Wai-Cheung & Wong, Heung & Zhang, Riquan, 2007. "Generalized likelihood ratio test for varying-coefficient models with different smoothing variables," Computational Statistics & Data Analysis, Elsevier, vol. 51(9), pages 4543-4561, May.
    2. Huang, Zhensheng & Pang, Zhen & Lin, Bingqing & Shao, Quanxi, 2014. "Model structure selection in single-index-coefficient regression models," Journal of Multivariate Analysis, Elsevier, vol. 125(C), pages 159-175.
    3. Wong, Heung & Zhang, Riquan & Leung, Bartholomew & Huang, Zhensheng, 2013. "Testing the significance of index parameters in varying-coefficient single-index models," Computational Statistics & Data Analysis, Elsevier, vol. 57(1), pages 297-308.
    4. Wenceslao González-Manteiga & Rosa Crujeiras, 2013. "An updated review of Goodness-of-Fit tests for regression models," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 22(3), pages 361-411, September.
    5. repec:wyi:journl:002087 is not listed on IDEAS
    6. Wong, Heung & Ip, Wai-cheung & Zhang, Riquan, 2008. "Varying-coefficient single-index model," Computational Statistics & Data Analysis, Elsevier, vol. 52(3), pages 1458-1476, January.
    7. Xia, Yingcun & Härdle, Wolfgang Karl & Linton, Oliver, 2009. "Optimal smoothing for a computationally and statistically efficient single index estimator," SFB 649 Discussion Papers 2009-028, Humboldt University Berlin, Collaborative Research Center 649: Economic Risk.
    8. Peter Malec, 2016. "A Semiparametric Intraday GARCH Model," Cambridge Working Papers in Economics 1633, Faculty of Economics, University of Cambridge.
    9. Pradeep Ravikumar & John Lafferty & Han Liu & Larry Wasserman, 2009. "Sparse additive models," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 71(5), pages 1009-1030, November.
    10. Suneel Babu Chatla, 2023. "Nonparametric inference for additive models estimated via simplified smooth backfitting," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 75(1), pages 71-97, February.
    11. Goldenshluger, Alexander, 2002. "Density Deconvolution in the Circular Structural Model," Journal of Multivariate Analysis, Elsevier, vol. 81(2), pages 360-375, May.
    12. Chuan-hua Wei & Chunling Liu, 2012. "Statistical inference on semi-parametric partial linear additive models," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 24(4), pages 809-823, December.
    13. Weichi Wu & Zhou Zhou, 2017. "Nonparametric Inference for Time-Varying Coefficient Quantile Regression," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 35(1), pages 98-109, January.
    14. Chuanhua Wei & Yubo Luo & Xizhi Wu, 2012. "Empirical likelihood for partially linear additive errors-in-variables models," Statistical Papers, Springer, vol. 53(2), pages 485-496, May.
    15. Bodhisattva Sen & Mary Meyer, 2017. "Testing against a linear regression model using ideas from shape-restricted estimation," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 79(2), pages 423-448, March.
    16. Tue Gørgens, 1999. "Semiparametric Estimation of Single-Index Transition Intensities," Discussion Papers 99-25, University of Copenhagen. Department of Economics.
    17. Linton, Oliver, 2002. "Edgeworth approximations for semiparametric instrumental variable estimators and test statistics," Journal of Econometrics, Elsevier, vol. 106(2), pages 325-368, February.
    18. Zambom, Adriano Zanin & Akritas, Michael G., 2015. "Nonparametric significance testing and group variable selection," Journal of Multivariate Analysis, Elsevier, vol. 133(C), pages 51-60.
    19. Ichimura, Hidehiko & Todd, Petra E., 2007. "Implementing Nonparametric and Semiparametric Estimators," Handbook of Econometrics, in: J.J. Heckman & E.E. Leamer (ed.), Handbook of Econometrics, edition 1, volume 6, chapter 74, Elsevier.
    20. Guo Shuang & Wei Chuanhua, 2015. "Testing for Spatial Lag Effects in Varying Coefficient Spatial Autoregressive Models," Journal of Systems Science and Information, De Gruyter, vol. 3(6), pages 561-567, December.
    21. Cai, Biqing & Cheng, Tingting & Yan, Cheng, 2018. "Time-varying skills (versus luck) in U.S. active mutual funds and hedge funds," Journal of Empirical Finance, Elsevier, vol. 49(C), pages 81-106.

    More about this item

    Keywords

    ;

    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:eee:jmvana:v:101:y:2010:i:4:p:1026-1041. 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.