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On the construction of efficient estimators in semiparametric models

Author

Listed:
  • Forrester Jeffrey S.
  • Hooper William J.
  • Peng Hanxiang
  • Schick Anton

Abstract

This paper deals with the construction of efficient estimators in semiparametric models without the sample splitting technique. Schick (1987) gave sufficient conditions using the leave-one-out technique for a construction without sample splitting. His conditions are stronger and more cumbersome to verify than the necessary and sufficient conditions for the existence of efficient estimators which suffice for the construction based on sample splitting. In this paper we use a conditioning argument to weaken Schick′s conditions. We shall then show that in a large class of semiparametric models and for properly chosen estimators of the score function the resulting weaker conditions reduce to the minimal conditions for the construction with sample splitting. In other words, in these models efficient estimators can be constructed without sample splitting under the same conditions as those used for the construction with sample splitting. We demonstrate our results by constructing an efficient estimator using these ideas in a semiparametric additive regression model.

Suggested Citation

  • Forrester Jeffrey S. & Hooper William J. & Peng Hanxiang & Schick Anton, 2003. "On the construction of efficient estimators in semiparametric models," Statistics & Risk Modeling, De Gruyter, vol. 21(2/2003), pages 109-138, February.
    • Handle: RePEc:bpj:strimo:v:21:y:2003:i:2/2003:p:109-138:n:2
    DOI: 10.1524/stnd.21.2.109.19007
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    References listed on IDEAS

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    1. Schick, Anton, 1996. "Root-n-consistent and efficient estimation in semiparametric additive regression models," Statistics & Probability Letters, Elsevier, vol. 30(1), pages 45-51, September.
    2. Anton Schick, 1998. "An Adaptive Estimator of the Autocorrelation Coefficient in Regression Models with Autoregressive Errors," Journal of Time Series Analysis, Wiley Blackwell, vol. 19(5), pages 575-589, September.
    3. Schick, Anton, 1996. "Efficient estimation in a semiparametric additive regression model with autoregressive errors," Stochastic Processes and their Applications, Elsevier, vol. 61(2), pages 339-361, February.
    4. Schick, Anton, 1999. "Efficient estimation of a shift in nonparametric regression," Statistics & Probability Letters, Elsevier, vol. 41(3), pages 287-301, February.
    5. Pollard, David, 1991. "Asymptotics for Least Absolute Deviation Regression Estimators," Econometric Theory, Cambridge University Press, vol. 7(2), pages 186-199, June.
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    Cited by:

    1. Wang, Xueqin & Peng, Hanxiang, 2008. "Moment estimation in a semiparametric generalized linear model," Statistics & Probability Letters, Elsevier, vol. 78(12), pages 1624-1633, September.
    2. Wu, Jingjing & Karunamuni, Rohana & Zhang, Biao, 2010. "Minimum Hellinger distance estimation in a two-sample semiparametric model," Journal of Multivariate Analysis, Elsevier, vol. 101(5), pages 1102-1122, May.
    3. Peng, Hanxiang & Schick, Anton, 2005. "Efficient estimation of linear functionals of a bivariate distribution with equal, but unknown marginals: the least-squares approach," Journal of Multivariate Analysis, Elsevier, vol. 95(2), pages 385-409, August.

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