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A nonparametric Cramer-Rao inequality for estimators of statistical functionals

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  • Janssen, Arnold

Abstract

The present paper introduces a lower bound for the mean quadratic error of estimators of differentiable statistical functionals. The result can be extended to bilinear covariance forms of vector-valued estimators. The lower bound leads to a concept of Fisher efficiency of estimators for functionals. The concept is based on tangent spaces and L2-differentiable submodels.

Suggested Citation

  • Janssen, Arnold, 2003. "A nonparametric Cramer-Rao inequality for estimators of statistical functionals," Statistics & Probability Letters, Elsevier, vol. 64(4), pages 347-358, October.
    • Handle: RePEc:eee:stapro:v:64:y:2003:i:4:p:347-358
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    Cited by:

    1. Arnold Janssen & Andreas Knoch, 2016. "Information bounds for nonparametric estimators of L-functionals and survival functionals under censored data," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 79(2), pages 195-220, February.

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