推 breadevil:mle不變性? 03/28 20:35
let X1,X2,...,Xn be a random sample from the uniformly distrubution.
f(x)=1/θ θ<x<2θ , θ>0.
Show that (1/2)Y1+(1/4)Yn is one mle of θ , where Y1,Y2,...Yn
represent the order statistics of the random sample.
這是我們的做法
1
likelihood function is L(θ)=-----I[(1/2)Yn,Y1](θ) where I is indictor
θ^n function.
明顯的 L(θ)為一個θ遞減函數 ,for all θ>0.
所以θ的mle為Yn
難以想像 為何(1/2)Y1+(1/4)Yn is one mle of θ ??
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