多元线性模型参数的有偏估计

A new class of biased estimate in the multiple linear model

文章对于多元线性模型Yn×q^(Xn×pBp×q,Vq×q In×n)提出了参数B的一种有偏估计^βh,^hβ在线性模型典则形式下,对应的有偏估计为^αh=(IqΛ+hI)-1(IqΛ+I)^α,此^αh有很好的统计性质;并阐明它在均方误差准则下这种估计相对于最小二乘估计和岭估计的优良性问题,从而推广了已有的有关结果。

The paper considers the multiple linear model Yn×q ～ （Xn×pBp×q ,gq×q × In×n） . A new biased estimate βh for the parameter B is given. In the canonical form of the linear model, flh is corresponding to the biased estimateαh = （Iq×A＋hI）^-1 （Iq×A＋I）d , and this estimate has good statistical properties. The superiority of βh over the least squares estimator of regression coefficients and the ridge estimate is studied in terms of the mean square error criterion. The result has extended related results.