关于可估函数LS估计相和条件的一个问题

On a Problem about the Consistency Condition of the LS Estimates of Estimable Functions

设有线性回归Yi=x'iβ0+ei,1≤i≤n,n≥1.本文在Sn=sum from i=1 to n xix'i的逆可以不存在的情况下,对任一特定的可估函数c'β0,给出了其LS估计为相合的充要条件.

Consider the linear regression Yi = x'iβ0+ei, 1≤ i≤ n, n ≥ 1. In this article, under the condition that Sn = sum from i=1 to n xix'i may have no inverse, we obtain the necessary and sufficient condition for any specified estimable function c'β0 whose LS estimate is consistent.