13. We have five unbiased estimators $\hat{\theta}_1, \hat{\theta}_2, \hat{\theta}_3, \hat{\theta}_4, \hat{\theta}_5$ of $\theta$. Given that $\sigma > 0$ and $n > 3$, the variance of the best estimator is (a) $V[\hat{\theta}_1] = 2\sigma^2 / (n - 1)$ (b) $V[\hat{\theta}_2] = 2\sigma^2 / n$ (c) $V[\hat{\theta}_3] = 2(n - 1)\sigma^2 / n^2$ (d) $V[\hat{\theta}_4] = 2\sigma^2$ (e) $V[\hat{\theta}_5] = 2\sigma^2 / 3$
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An unbiased estimator is a statistic that gives an estimate of a parameter without any systematic error. In other words, on average, the estimator gives the correct value of the parameter. In this question, we are given five unbiased estimators of 0, denoted as Show more…
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