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Efficient estimation in single-index regression

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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, 1997. "Efficient estimation in single-index regression," SFB 373 Discussion Papers 1997,37, Humboldt University of Berlin, Interdisciplinary Research Project 373: Quantification and Simulation of Economic Processes.
    • Handle: RePEc:zbw:sfb373:199737
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    References listed on IDEAS

    as
    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. Horowitz, Joel & Hardle, Wolfgang, 1994. "Direct Semiparametric Estimation of Single-Index Models With Discrete Covariates," Working Papers 94-22, University of Iowa, Department of Economics.
    3. 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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