一种新的有偏估计

A New Class of Biased Estimate

考虑线性回归模型Ｙ＝Ｘβ十ε，Ｅ（ε）＝０，ＣＯＶ（ε）＝σ２Ｉ。本文给出另一种形式的有偏估计以βｈ＝（Ｘ’Ｘ＋ｈＩ）－１（Ｘ’Ｙ十β），其中ｈ＞０是参数。β是回归系数β的ＬＳ估计，并阐明了βｈ也是一种好的估计。

Consider the linear regression model Y = Xβ + ε, E(ε ) = 0 andCOV(ε ) =σ2I. This paper gives another class of biased estimate βh =(X'X + hI)-1(X'Y + β ), where h> 0 is a parameter and β is the least squares estimate. It show that βh is also a good estimate.