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 $\infty$.
Citation
Hani Doss. Jayaram Sethuraman. "The Price of Bias Reduction when there is no Unbiased Estimate." Ann. Statist. 17 (1) 440 - 442, March, 1989. https://doi.org/10.1214/aos/1176347028
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