Estimation for Linear Models with Unequal Variances
Abstract This article considers the familiar linear model in which the residual vector e has elements e i with expectation 0 but different variances σ2 i . The elements of and the σ2 i are estimated by maximum likelihood under the assumption of a lower bound for the σ2 i of the form 0 < δ2 i ≤ σ2 i so that the likelihood is finite in the restricted parameter space. A second problem is considered in which the y vector splits into k sub-vector y j , such that all elements of y j have equal variances. Various asymptotic optimality properties and small sample unbiassedness for are proved.