[理工] 證明semipositive definite
X=[X1 X2 ..... Xp] (n*p matrix) n>p
1_n=[1 1 1 1 ... 1]' (n*1 vector)
X1=1_n X2 ... Xp are all n*1 vectors
H=X[(X'X)^-1]X'
1_n=[1 1 1 1 ... 1]' (n*1 vector)
1.proof that H-(1_n)*(1_n)'/n is semi positive definite
這一題我的證法是用迴歸去想
SSR=(yhat-ybar)'*(yhat-ybar)=y'*(-(1_n)*(1_n)'/n)y>=0
2.proof that diagonal elements of H ,h_i and h_i>=1/n
這一題我也是用迴歸去想h_i=1/n+(x_i-xbar)^2/Sxx
想請問如果要直接用線代的方法證該如何證呢?
--
※ 發信站: 批踢踢實業坊(ptt.cc)
◆ From: 61.227.244.105
※ 編輯: tokyo291 來自: 61.227.244.105 (02/06 00:57)
推
02/07 13:15, , 1F
02/07 13:15, 1F
→
02/07 13:15, , 2F
02/07 13:15, 2F