IDEAS home Printed from https://ideas.repec.org/a/eee/jmvana/v158y2017icp47-59.html
   My bibliography  Save this article

A new minimum contrast approach for inference in single-index models

Author

Listed:
  • Li, Weiyu
  • Patilea, Valentin

Abstract

Semiparametric single-index models represent an appealing compromise between parametric and nonparametric approaches and have been widely investigated in the literature. The underlying assumption in single-index models is that the information carried by the vector of covariates could be summarized by a one-dimensional projection. We propose a new, general inference approach for such models, based on a quadratic form criterion involving kernel smoothing. The approach could be applied with general single-index assumptions, in particular for mean regression models and conditional law models. The covariates could be unbounded and no trimming is necessary. A resampling method for building confidence intervals for the index parameter is proposed. Our empirical experiments reveal that the new method performs well in practice.

Suggested Citation

  • Li, Weiyu & Patilea, Valentin, 2017. "A new minimum contrast approach for inference in single-index models," Journal of Multivariate Analysis, Elsevier, vol. 158(C), pages 47-59.
    • Handle: RePEc:eee:jmvana:v:158:y:2017:i:c:p:47-59
    DOI: 10.1016/j.jmva.2017.03.009
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0047259X17301987
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.jmva.2017.03.009?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. Chiang, Chin-Tsang & Huang, Ming-Yueh, 2012. "New estimation and inference procedures for a single-index conditional distribution model," Journal of Multivariate Analysis, Elsevier, vol. 111(C), pages 271-285.
    2. Yu Y. & Ruppert D., 2002. "Penalized Spline Estimation for Partially Linear Single-Index Models," Journal of the American Statistical Association, American Statistical Association, vol. 97, pages 1042-1054, December.
    3. Jun Zhang & Zhenghui Feng & Peirong Xu, 2015. "Estimating the conditional single-index error distribution with a partial linear mean regression," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 24(1), pages 61-83, March.
    4. Powell, James L & Stock, James H & Stoker, Thomas M, 1989. "Semiparametric Estimation of Index Coefficients," Econometrica, Econometric Society, vol. 57(6), pages 1403-1430, November.
    5. Xiangrong Yin & R. Dennis Cook, 2002. "Dimension reduction for the conditional kth moment in regression," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 64(2), pages 159-175, May.
    6. Hall, Peter & Yao, Qiwei, 2005. "Approximating conditional distribution functions using dimension reduction," LSE Research Online Documents on Economics 16333, London School of Economics and Political Science, LSE Library.
    7. Kong, Efang & Xia, Yingcun, 2012. "A Single-Index Quantile Regression Model And Its Estimation," Econometric Theory, Cambridge University Press, vol. 28(4), pages 730-768, August.
    8. Lavergne, Pascal & Patilea, Valentin, 2013. "Smooth minimum distance estimation and testing with conditional estimating equations: Uniform in bandwidth theory," Journal of Econometrics, Elsevier, vol. 177(1), pages 47-59.
    9. Klein, Roger W & Spady, Richard H, 1993. "An Efficient Semiparametric Estimator for Binary Response Models," Econometrica, Econometric Society, vol. 61(2), pages 387-421, March.
    10. Delecroix, Michel & Härdle, Wolfgang & Hristache, Marian, 2003. "Efficient estimation in conditional single-index regression," Journal of Multivariate Analysis, Elsevier, vol. 86(2), pages 213-226, August.
    11. Efang Kong & Yingcun Xia, 2007. "Variable selection for the single‐index model," Biometrika, Biometrika Trust, vol. 94(1), pages 217-229.
    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. 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.

    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. Ming-Yueh Huang & Chin-Tsang Chiang, 2017. "Estimation and Inference Procedures for Semiparametric Distribution Models with Varying Linear-Index," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 44(2), pages 396-424, June.
    2. 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.
    3. Huybrechts F. Bindele & Ash Abebe & Karlene N. Meyer, 2018. "General rank-based estimation for regression single index models," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 70(5), pages 1115-1146, October.
    4. Catalina Bolancé & Ricardo Cao & Montserrat Guillen, 2018. "“Flexible maximum conditional likelihood estimation for single-index models to predict accident severity with telematics data”," IREA Working Papers 201829, University of Barcelona, Research Institute of Applied Economics, revised Dec 2018.
    5. Andrés Alonso & Ana Sipols & Silvia Quintas, 2013. "A single-index model procedure for interpolation intervals in time series," Computational Statistics, Springer, vol. 28(4), pages 1463-1484, August.
    6. Bucher, Axel & El Ghouch, Anouar & Van Keilegom, Ingrid, 2014. "Single-index quantile regression models for censored data," LIDAM Discussion Papers ISBA 2014001, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    7. Lai, Peng & Wang, Qihua & Lian, Heng, 2012. "Bias-corrected GEE estimation and smooth-threshold GEE variable selection for single-index models with clustered data," Journal of Multivariate Analysis, Elsevier, vol. 105(1), pages 422-432.
    8. Juan Carlos Escanciano & Kyungchul Song, 2007. "Asymptotically Optimal Tests for Single-Index Restrictions with a Focus on Average Partial Effects," PIER Working Paper Archive 07-005, Penn Institute for Economic Research, Department of Economics, University of Pennsylvania.
    9. Yang, Jing & Tian, Guoliang & Lu, Fang & Lu, Xuewen, 2020. "Single-index modal regression via outer product gradients," Computational Statistics & Data Analysis, Elsevier, vol. 144(C).
    10. Chiang, Chin-Tsang & Huang, Ming-Yueh, 2012. "New estimation and inference procedures for a single-index conditional distribution model," Journal of Multivariate Analysis, Elsevier, vol. 111(C), pages 271-285.
    11. Jianqing Fan & Yongyi Guo & Mengxin Yu, 2021. "Policy Optimization Using Semi-parametric Models for Dynamic Pricing," Papers 2109.06368, arXiv.org, revised May 2022.
    12. Chin-Shang Li & Minggen Lu, 2018. "A lack-of-fit test for generalized linear models via single-index techniques," Computational Statistics, Springer, vol. 33(2), pages 731-756, June.
    13. Weiyu Li & Valentin Patilea, 2018. "A dimension reduction approach for conditional Kaplan–Meier estimators," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 27(2), pages 295-315, June.
    14. Ming-Yueh Huang & Chin-Tsang Chiang, 2017. "An Effective Semiparametric Estimation Approach for the Sufficient Dimension Reduction Model," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 112(519), pages 1296-1310, July.
    15. Bousebata, Meryem & Enjolras, Geoffroy & Girard, Stéphane, 2023. "Extreme partial least-squares," Journal of Multivariate Analysis, Elsevier, vol. 194(C).
    16. Jiang, Rong & Zhou, Zhan-Gong & Qian, Wei-Min & Chen, Yong, 2013. "Two step composite quantile regression for single-index models," Computational Statistics & Data Analysis, Elsevier, vol. 64(C), pages 180-191.
    17. Jianbo Li & Yuan Li & Riquan Zhang, 2017. "B spline variable selection for the single index models," Statistical Papers, Springer, vol. 58(3), pages 691-706, September.
    18. Hall, Peter & Yao, Qiwei, 2005. "Approximating conditional distribution functions using dimension reduction," LSE Research Online Documents on Economics 16333, London School of Economics and Political Science, LSE Library.
    19. Qi Li & Jeffrey Scott Racine, 2006. "Nonparametric Econometrics: Theory and Practice," Economics Books, Princeton University Press, edition 1, volume 1, number 8355.
    20. Ai, Chunrong & Chen, Xiaohong, 2007. "Estimation of possibly misspecified semiparametric conditional moment restriction models with different conditioning variables," Journal of Econometrics, Elsevier, vol. 141(1), pages 5-43, November.

    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:158:y:2017:i:c:p:47-59. 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.