1980BiometrikaRequires access

The Welch-James approximation to the distribution of the residual sum of squares in a weighted linear regression

Søren Johansen

Open publisher page 199 citations

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).

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What this paper is about

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).

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OpenAlex reports 199 citations for this work. Citation counts describe recorded attention and do not establish research quality.

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Available 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).

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

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