Suppose that Y1, Y2, . . . , Yn constitute a
Chapter 9, Problem 104SE(choose chapter or problem)
Suppose that \(Y_{1}, Y_{2}, \ldots, Y_{n}\) constitute a random sample from the density function
\(f(y \mid \theta)=\left\{\begin{array}{ll} e^{-(y-\theta)}, & y>\theta \\ 0, & \text { elsewhere }
\end{array}\right.\)
where \(\theta\) is an unknown, positive constant.
a Find an estimator \(\widehat{\theta}_{1}\) for \(\theta\) by the method of moments.
b Find an estimator \(\widehat{\theta}_{2}\) for \(\theta\) by the method of maximum likelihood.
c Adjust \(\widehat{\theta}_{1} \text { and } \widehat{\theta}_{2}\) so that they are unbiased. Find the efficiency of the adjusted \(\widehat{\theta}_{1}\) relative to the adjusted \(\widehat{\theta}_{2}\).
Equation Transcription:
{
Text Transcription:
Y1, Y2,...,Yn
f(y \mid \theta)={e^-(y-\theta), & y>\theta \\ 0, elsewhere
\theta
\widehat\theta}_1
\theta
\widehat\theta}_2
\theta
\widehat\theta_1 and \widehat\theta_2
\widehat\theta}_1
\widehat\theta}_2
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