Some Remark about Consistency Problem of Parameter Estimation

摘要

Let Y_i = x'_iβ + e_i, 1 ≤ i ≤ n, n ≥ 1,be a linear regression model. Denote by λ_n and μ_n the smallest and largest eigenvalues of n∑i=1 x_ix'_i. Assume that the random errors e_1, e_2, … are iid, Ee_1 = 0 and E|e_1| < ∞. Under the restriction that μ_n = O(λ_n), this paper obtains the necessary and sufficient condition for the LS estimate of β to be strongly consistent.