Use the method described in Exercise 9.26 to show that, if
Chapter 9, Problem 27E(choose chapter or problem)
Use the method described in Exercise 9.26 to show that, if \(Y_{(1)}=\min \left(Y_{1}, Y_{2}, \ldots, Y_{n}\right)\) when \(Y_{1}, Y_{2}, \ldots, Y_{n}\) are independent uniform random variables on the interval \((0, \theta)\), then \(Y_{(1)}\) is not a consistent estimator for \(\theta\). [Hint: Based on the methods of Section 6.7, \(Y_{(1)}\) has the distribution function
\(F_{(1)}(y)=\left\{\begin{array}{ll}0, & y<0 \\1-(y / \theta)^{n}, & 0 \leq y \leq 8, \\1, & y>\theta .]\end{array}\right.\)
Equation Transcription:
= min
{
Text Transcription:
Y_(1) = min (Y_1, Y_2, …., Y_n)
Y_1, Y_2, …., Y_n
(0, theta)
Y_(1)
theta
Y_(1)
F_{(1)}(y) = {0, & y < 0 \\1- (y / theta)^{n}, & 0 leq y leq 8, \\1, & y > theta .]
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