[整理版]误差项方差无偏估计量
Estimating the Error Variance
估计误差方差
22,First, we notice ,=E(u), therefore, an unbiased
n22 estimator of ,is (1/n)u,ii,1
222首先,我们注意到=E(u), 所以的无偏估,,
n2(1/n)u计量是,ii,1
,uis not observable, but we can find an unbiased i
estimator for ui.
u是不可观测的,但我们能够找到一个的无偏uii
估计量
Error Variance Estimate (cont)
误差方差估计量(继续)
,,ˆˆˆu,y,,xii01i
,,,,ˆˆ,,,,x,u,,x01ii01i
ˆˆ,,,,,,,,,u,,,,i0011
2,Then, an unbiased estimator of is
2,那么,的一个无偏估计量是
122ˆˆ,,,,u,SSR/n,2,i
,,n,2
ˆProof: Using the fact that u,0 we get
,,,,ˆˆˆu-(,),(,)x,0, substracting it from the u equation,0011i
,,ˆˆu,(u,u)-(,)(x,x). ii11i
Therefore,
2,,,,222ˆˆˆu,(u,u),(,)(x,x),2(,)u(x,x),,,,ii11i11ii
22,We have E((u,u)),(n,1),,i
222,,,ˆE{(,)(x,x)},, and because,11i
2ˆ,,,,(u(x,x))/(x,x),,,11iii
2ˆ,,,E{2(,)u(x,x)},2,,ii11
22ˆHence E(u),(n,2),.,i