艾特肯线性最小二乘法Aitken's linear least square mothod 发表评论(0) 编辑词条

       Generalized least squares (GLS)is a method for fitting coefficients of explanatory variables that help to predict the outcomes of a dependent random variable. As its name suggests, GLS includes ordinary least squares (OLS) as a special case. GLS is also called "Aitken’s estimator," after A. C. Aitken (1935). The principal motivation for generalizing OLS is the presence of covariance among the observations of the dependent variable or of different variances across these observations, conditional on the explanatory variables. Both phenomena lead to problems with statistical inference procedures commonly used with OLS. Most critically, the standard methods for estimating sampling variances and testing hypotheses become biased. In addition, the OLS-fitted coefficients are inaccurate relative to the GLS-fitted coefficients.
In its simplest form, the linear model of statistics postulates the existence of a linear conditional expectation for a scalar, dependent random variable y given a set of non-random scalar explanatory variables {x,, …, xJ: