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Unformatted text preview: 8-16Solutions Manual for Statistical InferenceWe now choose the constantcto achieve size, and wereject if|x-|> tn-1,/2ps2/n.c. Again, see Chapter 5 of Lehmann (1986).8.39 a. From Exercise 4.45c,Wi=Xi-Yin(W,2W), whereX-Y=Wand2X+2Y-XY=2W. TheWis are independent because the pairs (Xi,Yi) are.b. The hypotheses are equivalent toH:W= 0 vsH1:W6= 0, and, from Exercise 8.38, ifwe rejectHwhen|W|> tn-1,/2pS2W/n, this is the LRT (based onW1,...,Wn) of size. (Note that if >0, VarWican be small and the test will have good power.)8.41 a.(x,y) =supHL(X,Y,2|x,y)supL(X,Y,2|x,y)=L(,2|x,y)L(X,Y,21|x,y).UnderH, theXis andYis are one sample of sizem+nfrom a n(,2) population, where=X=Y. So the restricted MLEs are=iXi+iYin+m=nx+nyn+mand2=i(Xi-)2+i(Yi-)2n+m.To obtain the unrestricted MLEs, x, y, 2, useL(X,Y,2|x,y) = (22)-(n+m)/2e-[i(xi-X)2+i(yi-Y)2]/22....
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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.
- Spring '12