Invariance Properties of Uncorrelated Residual Transformations
不相关残差变换的不变性
Summary The problem of obtaining an uncorrelated residual in the general linear model of full rank which is orthogonal to the design matrix has been discussed by Theil (1965), Brown et al. (1975) and others. In this paper it is shown that the problem is equivalent to stipulating an invariance requirement for the corresponding residual sum of squares, thus implying that alternative uncorrelated residuals are necessarily related by an orthogonal transformation. The set of…