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The Price of Bias Reduction when there is no Unbiased Estimate

Hani Doss, Jayaram Sethuraman

The Annals of Statistics · 1989 · Volume 17 · Issue 1

DOI: 10.1214/aos/1176347028

Abstract

Let $\phi$ be a parameter for which there is no unbiased estimator. This note shows that for an arbitrary sequence of estimators $T^{(k)}$, if the biases of $T^{(k)}$ tend to 0 then their variances must tend to $\infty$.

Keywords

62A99, 62F11, bias reduction, bootstrap estimate of bias, jackknife estimate of bias

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