Dr. Hackney STA Solutions pg 146

Dr. Hackney STA Solutions pg 146 - 9-4Solutions 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: 9-4Solutions Manual for Statistical InferenceThe LRT statistic is(x) =aan/2e-12a(xi-)2e-12a(xi-)2=12an/2en/2e-12a(xi-)2The rejection region of a sizetest is{x:(x)c}, and a 1-confidence set is{a:(x)c}.b. Using the results of Exercise 8.8b, the restricted MLE (fora=a) is found by solving-a2+ [2+ (x-)2] +(x-) = 0,yielding the MLER= x+px+ 4a(2+ x2)/2a.The unrestricted MLEs are= xanda=1nx2nXi=1(xi-x)2=2x2,yielding the LRT statistic(x) =/Rne(n/2)-(xi-R)2/(2R).The rejection region of a sizetest is{x:(x)c}, and a 1-confidence set is{a:(x)c}.9.9 LetZ1,...,Znbe iid with pdff(z).a. ForXif(x-), (X1,...,Xn)(Z1+,...,Zn+), andX-Z+-=Z. Thedistribution ofZdoes not depend on.b. ForXif(x/)/, (X1,...,Xn)(Z1,...,Zn), andX/Z/=Z. The distribu-tion ofZdoes not depend on....
View Full Document

This note was uploaded on 02/03/2012 for the course STA 1014 taught by Professor Dr.hackney during the Spring '12 term at UNF.

Ask a homework question - tutors are online