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Efficient estimation in conditional single-index regression

Author

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

Abstract

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

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    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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    1. repec:spr:testjl:v:27:y:2018:i:2:d:10.1007_s11749-017-0546-2 is not listed on IDEAS
    2. repec:eee:jmvana:v:158:y:2017:i:c:p:47-59 is not listed on IDEAS
    3. 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.
    4. repec:spr:compst:v:32:y:2017:i:3:d:10.1007_s00180-017-0726-2 is not listed on IDEAS
    5. repec:bla:scjsta:v:44:y:2017:i:2:p:396-424 is not listed on IDEAS
    6. 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.
    7. 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.
    8. 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.
    9. 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.
    10. 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.
    11. Donkers, Bas & Schafgans, Marcia M. A., 2005. "A method of moments estimator for semiparametric index models," LSE Research Online Documents on Economics 6815, London School of Economics and Political Science, LSE Library.
    12. 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.
    13. 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.
    14. 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.
    15. 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.
    16. 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.
    17. 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.
    18. 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.
    19. 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.
    20. 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.
    21. 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.
    22. 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.
    23. repec:spr:compst:v:33:y:2018:i:2:d:10.1007_s00180-018-0802-2 is not listed on IDEAS
    24. 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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