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

摘要: 设有线性回归Y_i=x'_iβ₀+e_i,1≤i≤n,n≥1.本文在S_n=sum from i=1 to n x_ix'_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.

Abstract: Consider the linear regression Y_i = x'_iβ₀+e_i, 1≤i≤n,n≥1. In this article, under the condition that S_n = 1 to n x_ix'_i may have no inverse, we obtain the necessary and sufficient condition for any specified estimable functionc'β₀ whose LS estimate is consistent.