Hani Doss, Jayaram Sethuraman
Abstract
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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 $\infty$.
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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 $\infty$.
Key concepts: Mathematics, Bias of an estimator, Unbiased Estimation, U-statistic, Estimator, Minimum-variance unbiased estimator, Best linear unbiased prediction, Stein's unbiased risk estimate