Hello, I’m look for some help on how to solve this problem.
Let f(x; ) = g( )h(x), , where a( decreases and b( ) increases with . Suppose g() is a differentiable function of and that we have a random sample from this pdf. Let be the corresponding order statistics.
a) Show that S = max ( is a sufficient statistic for
b) Prove then that the Minimum Variance Unbiased Estimator of is
c) Show that P(S;) = is a pivotal quantity and then derive its distribution
d) Use the pivotal quantity P(S;) above to obtain a 100(1- )% confidence interval for g() of the form ( ) and explain how you will determine the constants