Let the pdf f(x; 1 , 2 ) be of the form exp[p 1 (

Question:

Let the pdf f(x; θ1, θ2) be of the form

exp[p11, θ2)K1(x) + p21, θ2)K2(x) + H(x) + q11, θ2)], a < x < b,
zero elsewhere. Suppose that K'1(x) = cK'2(x). Show that f(x; θ1, θ2) can be written in the form
exp[p(θ1, θ2)K2(x) + H(x) + q(θ1, θ2)], a < x < b,
zero elsewhere. This is the reason why it is required that no one K'j(x) be a linear homogeneous function of the others, that is, so that the number of sufficient statistics equals the number of parameters.

Fantastic news! We've Found the answer you've been seeking!

Step by Step Answer:

Related Book For  book-img-for-question

Introduction To Mathematical Statistics

ISBN: 9780321794710

7th Edition

Authors: Robert V., Joseph W. McKean, Allen T. Craig

Question Posted: