摘要
本文考虑一般线性模型:Y=Xβ+ε,其中向量Y不能直接观测到,而只能观测到T=A′Y,这里A是任意的n×m阶矩阵。我们提出了系统β的一种新的有偏估计,在均方误差(MSE)准则下,我们证明了这种有偏估计可优于文献中经常提出的基于聚集数据的最优线性无偏估计,甚至也可优于无聚集的Gauss-Markov估计,与文献[3]提出的“朴实”最小二乘(NLS)估计相比较,这种有偏估计是一种更适当的估计。
In this paper, we propose a biased estimator of β after our careful study on the general regression model: Y = Xβ+ε, where the variable Y is substituted by T = A'Y , and A is an n × m matrix. According to the mean square error (MSE) matices, we have proved that the biased estimator may even perform better than the Gauss-Morkov estimator based on untransformed data. It may be reasonable to use the biased estimator proposed in this paper instead of the 'Naive' LS (NLS) estimator proposed in paper [3].