Dr. Hackney STA Solutions pg 169

Dr. Hackney STA Solutions pg 169 - 10-12 Solutions Manual...

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10-12 Solutions Manual for Statistical Inference Underlying pdf Test θ 0 θ 0 + . 25 σ θ 0 + . 5 σ θ 0 + . 75 σ θ 0 + 1 σ θ 0 + 2 σ Laplace Naive 0 . 101 0 . 366 0 . 774 0 . 957 0 . 993 1 . Boot 0 . 097 0 . 364 0 . 749 0 . 932 0 . 986 1 . Median 0 . 065 0 . 245 0 . 706 0 . 962 0 . 995 1 . Logistic Naive 0 . 137 0 . 341 0 . 683 0 . 896 0 . 97 1 . Boot 0 . 133 0 . 312 0 . 641 0 . 871 0 . 967 1 . Median 0 . 297 0 . 448 0 . 772 0 . 944 0 . 993 1 . Normal Naive 0 . 168 0 . 316 0 . 628 0 . 878 0 . 967 1 . Boot 0 . 148 0 . 306 0 . 58 0 . 836 0 . 957 1 . Median 0 . 096 0 . 191 0 . 479 0 . 761 0 . 935 1 . Here is Mathematica code: This program calculates size and power for Exercise 10.39, Second Edition We do our calculations assuming normality, but simulate power and size under other distri- butions. We test H 0 : θ = 0 . theta_0=0; Needs["Statistics‘Master‘"] Clear[x] f1[x_]=PDF[NormalDistribution[0,1],x]; F1[x_]=CDF[NormalDistribution[0,1],x]; f2[x_]=PDF[LogisticDistribution[0,1],x]; f3[x_]=PDF[LaplaceDistribution[0,1],x]; v1=Variance[NormalDistribution[0,1]]; v2=Variance[LogisticDistribution[0,1]]; v3=Variance[LaplaceDistribution[0,1]]; Calculate m-estimate Clear[k,k1,k2,t,x,y,d,n,nsim,a,w1] ind[x_,k_]:=If[Abs[x]<k,1,0] rho[y_,k_]:=ind[y,k]*y^2 + (1-ind[y,k])*(k*Abs[y]-k^2)
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