Least Squares Estimation when the Covariance Matrix and Parameter Vector are Functionally Related
研究了线性模型中协方差矩阵对角元素是解释变量和未知参数的函数时，提出一种加权联合最小二乘估计量，其渐近等价于最大似然估计，并通过抽样实验比较了不同估计量的表现。
Abstract Estimation for the linear model y = Xβ + e with unknown diagonal covariance matrix G is considered. The diagonal elements of G are assumed to be known functions of the explanatory variables X and an unknown parameter vector Θ, where Θ is permitted to contain elements of β. A weighted joint least squares estimator is developed that is asymptotically equivalent to the maximum likelihood estimator. Asymptotic properties of the simple least squares estimator and of the weighted joint least squares estimator are obtained. A sampling experiment is used to compare the estimators.