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Efficient estimation in conditional single-index regression


  • Delecroix, Michel
  • Härdle, Wolfgang
  • Hristache, Marian


Semiparametric single-index regression involves an unknown finite-dimensional parameter and an unknown (link) function. We consider estimation of the parameter via the pseudo-maximum likelihood method. For this purpose we estimate the conditional density of the response given a candidate index and maximize the obtained likelihood. We show that this technique of adaptation yields an asymptotically efficient estimator: it has minimal variance among all estimators.

Suggested Citation

  • 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.
  • Handle: RePEc:eee:jmvana:v:86:y:2003:i:2:p:213-226

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    References listed on IDEAS

    1. 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.
    2. Newey, Whitney K & Stoker, Thomas M, 1993. "Efficiency of Weighted Average Derivative Estimators and Index Models," Econometrica, Econometric Society, vol. 61(5), pages 1199-1223, September.
    3. 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.
    4. Sherman, Robert P., 1994. "U-Processes in the Analysis of a Generalized Semiparametric Regression Estimator," Econometric Theory, Cambridge University Press, vol. 10(02), pages 372-395, June.
    5. Sherman, Robert P, 1993. "The Limiting Distribution of the Maximum Rank Correlation Estimator," Econometrica, Econometric Society, vol. 61(1), pages 123-137, January.
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    3. repec:bla:scjsta:v:44:y:2017:i:2:p:396-424 is not listed on IDEAS
    4. Yin, Xiangrong & Li, Bing & Cook, R. Dennis, 2008. "Successive direction extraction for estimating the central subspace in a multiple-index regression," Journal of Multivariate Analysis, Elsevier, vol. 99(8), pages 1733-1757, September.
    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. Kortelainen, Mika, 2008. "Estimation of semiparametric stochastic frontiers under shape constraints with application to pollution generating technologies," MPRA Paper 9257, University Library of Munich, Germany.
    7. Graciela Boente & Daniela Rodriguez, 2012. "Robust estimates in generalized partially linear single-index models," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 21(2), pages 386-411, June.
    8. Attaoui, Said & Laksaci, Ali & Ould Said, Elias, 2011. "A note on the conditional density estimate in the single functional index model," Statistics & Probability Letters, Elsevier, vol. 81(1), pages 45-53, January.
    9. Bas Donkers & Marcia M Schafgans, 2005. "A method of moments estimator for semiparametric index models," STICERD - Econometrics Paper Series 493, Suntory and Toyota International Centres for Economics and Related Disciplines, LSE.
    10. Lu, Xuewen, 2010. "Asymptotic distributions of two "synthetic data" estimators for censored single-index models," Journal of Multivariate Analysis, Elsevier, vol. 101(4), pages 999-1015, April.
    11. Minggen Lu & Chin-Shang Li, 2016. "Spline-based semiparametric estimation of a zero-inflated Poisson regression single-index model," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 68(5), pages 1111-1134, October.
    12. Ai, Chunrong & You, Jinhong & Zhou, Yong, 2011. "Statistical inference using a weighted difference-based series approach for partially linear regression models," Journal of Multivariate Analysis, Elsevier, vol. 102(3), pages 601-618, March.
    13. 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.
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    15. repec:eee:jmvana:v:158:y:2017:i:c:p:47-59 is not listed on IDEAS
    16. 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.
    17. 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.
    18. You, Jinhong & Zhou, Xian & Zhou, Yong, 2010. "Statistical inference for panel data semiparametric partially linear regression models with heteroscedastic errors," Journal of Multivariate Analysis, Elsevier, vol. 101(5), pages 1079-1101, May.
    19. Zhou, Xiao-Hua & Liang, Hua, 2006. "Semi-parametric single-index two-part regression models," Computational Statistics & Data Analysis, Elsevier, vol. 50(5), pages 1378-1390, March.
    20. Escanciano, Juan Carlos & Song, Kyungchul, 2010. "Testing single-index restrictions with a focus on average derivatives," Journal of Econometrics, Elsevier, vol. 156(2), pages 377-391, June.
    21. Said Attaoui, 2014. "Strong uniform consistency rates and asymptotic normality of conditional density estimator in the single functional index modeling for time series data," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 98(3), pages 257-286, July.
    22. Chen, Tao & Parker, Thomas, 2014. "Semiparametric efficiency for partially linear single-index regression models," Journal of Multivariate Analysis, Elsevier, vol. 130(C), pages 376-386.
    23. 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.
    24. repec:spr:compst:v:33:y:2018:i:2:d:10.1007_s00180-018-0802-2 is not listed on IDEAS
    25. Haibo Zhou & Jinhong You & Bin Zhou, 2010. "Statistical inference for fixed-effects partially linear regression models with errors in variables," Statistical Papers, Springer, vol. 51(3), pages 629-650, September.


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