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On universal unbiasedness of delta estimators

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Abstract

This paper considers delta estimators of a Radon-Nicodym derivative of a probability function with respect to a measure. Sufficient conditions for asymptotic unbiasedness and global rates of convergence, which can be improved by imposing differentiability conditions on the estimated curves, are provided. A bias reduction technique is proposed, and the application of the results to regression estimation is discussed. The sufficient conditions for asymptotic unbiasedness are checked for some broad classes of nonparametric estimators.

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  • Vidal-Sanz, Jose M., 1999. "On universal unbiasedness of delta estimators," DES - Working Papers. Statistics and Econometrics. WS 6322, Universidad Carlos III de Madrid. Departamento de Estadística.
    • Handle: RePEc:cte:wsrepe:6322
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    1. Robinson, Peter M, 1988. "Root- N-Consistent Semiparametric Regression," Econometrica, Econometric Society, vol. 56(4), pages 931-954, July.
    2. González-Manteiga, Wenceslao, 1998. "Significance testing in nonparametric regression base on the bootstrap," DES - Working Papers. Statistics and Econometrics. WS 6264, Universidad Carlos III de Madrid. Departamento de Estadística.
    3. 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.
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    Keywords

    Bias of delta estimators;

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