The Welch-James approximation to the distribution of the residual sum of squares in a weighted linear regression
Søren Johansen
Abstract
Søren Johansen
Abstract
A general discussion is given of the approximate distribution of the residual sum of squares in a linear model in which a weighted analysis is made with weights estimated empirically as the reciprocals of variance estimates. Applications to testing hypotheses are made and various generalizations indicated. The initial results simplify those of James (1951, 1954).
OpenAlex reports 199 citations for this work. Citation counts describe recorded attention and do not establish research quality.
A contribution statement is not available in the OpenAlex record.
Method details are not available in the OpenAlex metadata.
Findings are not separately available in the OpenAlex metadata.
Limitations are not available in the OpenAlex metadata.
Application details are not available in the OpenAlex metadata.
A general discussion is given of the approximate distribution of the residual sum of squares in a linear model in which a weighted analysis is made with weights estimated empirically as the reciprocals of variance estimates. Applications to testing hypotheses are made and various generalizations indicated. The initial results simplify those of James (1951, 1954).
Key concepts: Mathematics, Total sum of squares, Lack-of-fit sum of squares, Residual, Residual sum of squares, Explained sum of squares, Statistics, Generalized least squares