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Dr. Hackney STA Solutions pg 110

Dr. Hackney STA Solutions pg 110 - Second Edition 7-13 ^...

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Second Edition 7-13 The MLEs from the full data set are ˆ β = 0 . 0008413892 and ˆ τ = (0 . 06337310 , 0 . 06374873 , 0 . 06689681 , 0 . 04981487 , 0 . 04604075 , 0 . 04883109 , 0 . 07072460 , 0 . 01776164 , 0 . 03416388 , 0 . 01695673 , 0 . 02098127 , 0 . 01878119 , 0 . 05621836 , 0 . 09818091 , 0 . 09945087 , 0 . 05267677 , 0 . 08896918 , 0 . 08642925) . The MLEs for the incomplete data were computed using R , where we take m = x i . The R code is #mles on the incomplete data# xdatam<-c(3560,3739,2784,2571,2729,3952,993,1908,948,1172, 1047,3138,5485,5554,2943,4969,4828) ydata<-c(3,4,1,1,3,1,2,0,2,0,1,3,5,4,6,2,5,4) xdata<-c(mean(xdatam),xdatam); for (j in 1:500) { xdata<-c(sum(xdata)*tau[1],xdatam) beta<-sum(ydata)/sum(xdata) tau<-c((xdata+ydata)/(sum(xdata)+sum(ydata))) } beta tau The MLEs from the incomplete data set are ˆ β = 0 . 0008415534 and ˆ τ = (0 . 06319044 , 0 . 06376116 , 0 . 06690986 , 0 . 04982459 , 0 . 04604973 , 0 . 04884062 , 0 . 07073839 , 0 . 01776510 , 0 . 03417054 , 0 . 01696004 , 0 . 02098536 , 0 . 01878485 , 0 . 05622933 , 0 . 09820005 , 0 . 09947027 , 0 . 05268704 , 0 . 08898653 , 0 . 08644610) . 7 . 31 a. By direct substitution we can write log L ( θ | y ) = E log L ( θ | y , X ) | ˆ θ ( r ) , y - E log k ( X | θ, y ) | ˆ θ ( r ) , y . The next iterate, ˆ θ ( r +1) is obtained by maximizing the expected complete-data log likelihood, so for any
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