{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

Dr. Hackney STA Solutions pg 133

Dr. Hackney STA Solutions pg 133 - 8-12Solutions Manual for...

Info iconThis preview shows page 1. Sign up to view the full content.

View Full Document Right Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: 8-12Solutions Manual for Statistical Inference8.26 a. We will prove the result for continuous distributions. But it is also true for discrete MLRfamilies. Forθ1> θ2, we must showF(x|θ1)≤F(x|θ2). Nowddx[F(x|θ1)-F(x|θ2)] =f(x|θ1)-f(x|θ2) =f(x|θ2)f(x|θ1)f(x|θ2)-1.Becausefhas MLR, the ratio on the right-hand side is increasing, so the derivative can onlychange sign from negative to positive showing that any interior extremum is a minimum.Thus the function in square brackets is maximized by its value at∞or-∞, which is zero.b. From Exercise 3.42, location families are stochastically increasing in their location param-eter, so the location Cauchy family with pdff(x|θ) = (π[1+(x-θ)2])-1is stochasticallyincreasing. The family does not have MLR.8.27 Forθ2> θ1,g(t|θ2)g(t|θ1)=c(θ2)c(θ1)e[w(θ2)-w(θ1)]twhich is increasing intbecausew(θ2)-w(θ1)>0. Examples include n(θ,1), beta(θ,1), andBernoulli(θ)....
View Full Document

{[ snackBarMessage ]}

Ask a homework question - tutors are online