推 jackdan:強者~ 01/22 16:57
推 JimCroce:THX!!!寫太快了 01/22 17:19
→ JimCroce:沒注意到....= = 01/22 17:20
推 JimCroce:答案應該是N(0,1/2) ^^ 01/22 17:22
推 Jordan23:THX!!!寫太快了 沒注意到....= =
※ 編輯: Jordan23 來自: 61.224.79.249 (01/22 21:07)
※ 引述《JimCroce (我要下五子棋 N )》之銘言：
: ※ 引述《H0NEYCAT ()》之銘言：
: : Let Sn have a Chi-square distribution. Show that the
: : limiting distribution of √Sn - √n is N(0,1/2).
: : This is known as Fisher's approximation.
: : 拜託了
: E(Sn)=n Var(Sn)=2n
: by CLT 可知
: d
: (Sn - n) ---> N(0,2n)
收斂到一個還包含有n的東西, 有點怪.
by CTL (Not trivival)
n^(-0.5)(Sn-n)--->N(0,2) (in distribution)
n^(0.5)(Sn/n-1)--->N(0,2) (in distribution)
令g(x)=√x g在1連續
by delta method
n^(0.5)(g(Sn/n)-g(1))--->N(0,(g'(1))^2*2) (in distribution)
所以√Sn - √n--->N(0,1/2) (in distribution)
: by Cramer-δ theorem 令g(x)= √x , 且 在 x=n 連續
: d
: (√Sn - √n) --->g'(n) N(0,2n)≡N(0,1/2)
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