多元回归系数强相会估计的一些新结果(Ⅰ)(英文)

Some New Results of the Strong Consistency of Multiple Regression Coefficients(Ⅰ)

设有线性模型，假定随机误差e1，e2，…独立同分布，E（e1）＝0，E｜er｜＜∞对某个r∈（1，2）．本文在较弱的限制条件下，得到β的最小二乘估计为强相合的一些新结果．

Let be a linear regression model. Denote by λn and μn the smallest and largest eigenvalues of Assume that the random errors e1,,e2,···are iid., Ee1 =0 and E|e1|r<∞. Under the restriction that μn =0 (λn), this paper obtains the necessary and sufficient condition for the LS estimate of β to be strongly consistent.