| Suppose given a linear model yj=x'jβ+μj, j=1,2,…, The random errors all have a mean zero and unknown variance σ2, 0<σ2<∞. Let σn2 be the estimate of σ2 based on the residual sum of squares and calculated from (xj, yj), j=1,…,n. In this paper we show that if μ1,μ2,…, are independent but not necessarily identically distributed, and some further conditions on {μj} and (x1|…|xn) are satisfied, then for any ε>0 there exist constant ρε, 0<ρε<1, Such that P(|σn2-σ2|≥ε)=O(ρεn). |
