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Semiparametric efficiency for partially linear single-index regression models

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  • Chen, Tao
  • Parker, Thomas

Abstract

We calculate semiparametric efficiency bounds for a partially linear single-index model using a simple method developed by Severini and Tripathi (2001). We show that this model can be used to evaluate the efficiency of several existing estimators.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:jmvana:v:130:y:2014:i:c:p:376-386
    DOI: 10.1016/j.jmva.2014.06.006
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    References listed on IDEAS

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    1. Lee, Sokbae, 2003. "Efficient Semiparametric Estimation Of A Partially Linear Quantile Regression Model," Econometric Theory, Cambridge University Press, vol. 19(1), pages 1-31, February.
    2. Chen, Xiaohong & Pouzo, Demian, 2009. "Efficient estimation of semiparametric conditional moment models with possibly nonsmooth residuals," Journal of Econometrics, Elsevier, vol. 152(1), pages 46-60, September.
    3. Xiaohong Chen & Demian Pouzo, 2012. "Estimation of Nonparametric Conditional Moment Models With Possibly Nonsmooth Generalized Residuals," Econometrica, Econometric Society, vol. 80(1), pages 277-321, January.
    4. Newey, Whitney K. & Powell, James L., 1990. "Efficient Estimation of Linear and Type I Censored Regression Models Under Conditional Quantile Restrictions," Econometric Theory, Cambridge University Press, vol. 6(3), pages 295-317, September.
    5. Wu, Tracy Z. & Yu, Keming & Yu, Yan, 2010. "Single-index quantile regression," Journal of Multivariate Analysis, Elsevier, vol. 101(7), pages 1607-1621, August.
    6. Severini, Thomas A. & Tripathi, Gautam, 2013. "Semiparametric Efficiency Bounds for Microeconometric Models: A Survey," Foundations and Trends(R) in Econometrics, now publishers, vol. 6(3-4), pages 163-397, December.
    7. Zhao, Quanshui, 2001. "Asymptotically Efficient Median Regression In The Presence Of Heteroskedasticity Of Unknown Form," Econometric Theory, Cambridge University Press, vol. 17(4), pages 765-784, August.
    8. Van Keilegom, Ingrid & Wang, Lan, 2010. "Semiparametric modeling and estimation of heteroscedasticity in regression analysis of cross-sectional data," LIDAM Reprints ISBA 2010001, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    9. Ichimura, Hidehiko & Lee, Sokbae, 2010. "Characterization of the asymptotic distribution of semiparametric M-estimators," Journal of Econometrics, Elsevier, vol. 159(2), pages 252-266, December.
    10. 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.
    11. 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.
    12. Thomas A Severini & Gautam Tripathi, 2013. "A survey of semiparametric efficiency bounds for some microeconometric models," DEM Discussion Paper Series 13-10, Department of Economics at the University of Luxembourg.
    13. Koenker,Roger, 2005. "Quantile Regression," Cambridge Books, Cambridge University Press, number 9780521845731, January.
    14. repec:hal:journl:peer-00741628 is not listed on IDEAS
    15. Severini, Thomas A. & Tripathi, Gautam, 2001. "A simplified approach to computing efficiency bounds in semiparametric models," Journal of Econometrics, Elsevier, vol. 102(1), pages 23-66, May.
    16. 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.
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    Cited by:

    1. Ying-Ying Lee, 2015. "Interpretation and Semiparametric Efficiency in Quantile Regression under Misspecification," Econometrics, MDPI, vol. 4(1), pages 1-14, December.

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