Solved: Suppose that Y1, Y2, . . . , Yn denote a random
Chapter 9, Problem 7E(choose chapter or problem)
Suppose that \(Y_{1}, Y_{2}, \ldots, Y_{n}\) denote a random sample of size \(n\) from an exponential distribution with density function given by
\(f(y)=\left\{\begin{array}{lc}(1 / \theta) e^{-y / \theta}, & 0<y, \\0, & \text { elsewhere }\end{array}\right.\)
In Exercise 8.19, we determined that \(\hat{\theta}_{1}=n Y_{(1)}\) is an unbiased estimator of \(\theta\) with MSE \(\left(\hat{\theta}_{1}\right)=\theta^{2}\). Consider the estimator \(\hat{\theta}_{2}=\bar{Y}\) and find the efficiency of \(\hat{\theta}_{1}\) relative to \(\hat{\theta}_{2}\).
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