Solved: Let Y1, Y2, . . . , Yn denote a random sample from

QUESTION:

Let \(Y_{1}, Y_{2}, \ldots, Y_{n}\) denote a random sample from the uniform distribution on the interval \((\theta, \theta+1)\). Let

\(\hat{\theta}_{1}=\bar{Y}-\frac{1}{2}\) and \(\hat{\theta}_{2}=Y_{(n)}-\frac{n}{n+1}\)

a Show that both \(\hat{\theta}_{1}\) and \(\hat{\theta}_{2}\) are unbiased estimators of \(\theta\).

b Find the efficiency of \(\hat{\theta}_{1}\) relative to \(\hat{\theta}_{2}\).

Equation Transcription:

 =  -

 =

Text Transcription:

Y_1, Y_2,..., Y_n

(theta, theta + 1)

hat{theta}_1 = bar{Y} - frac{1}{2}

hat{theta}_1

hat{theta}_2

hat{theta}_2 =Y_{(n)} - frac{n}{n+1}

theta

hat{theta}_1

hat{theta}_2