Suppose that Y1, Y2, . . . , Yn is a random sample from a
Chapter 9, Problem 5E(choose chapter or problem)
Suppose that \(Y_{1}, Y_{2}, \ldots, Y_{n}\) is a random sample from a normal distribution with mean \(\mu\) and variance \(\sigma^{2}\). Two unbiased estimators of \(\sigma^{2}\) are
\(\hat{\sigma}_{1}^{2}=S^{2}=\frac{1}{n-1} \sum_{i=1}^{n}\left(Y_{i}-\bar{Y}\right)^{2}\) and \(\hat{\sigma}_{2}^{2}=\frac{1}{2}\left(Y_{1}-Y_{2}\right)^{2}\)
Find the efficiency of \(\hat{\sigma}_{1}^{2}\) relative to \(\hat{\sigma}_{2}^{2}\):
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