New Estimators of Disturbances in Regression Analysis

Abrahamse, A. P. J.; Koerts, J.

doi:10.1080/01621459.1971.10482221

Cited by 34 publications

(27 citation statements)

References 6 publications

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“…The proposition parallels a related result of Abrahamse and Koerts (1971). For completeness, we also sketch the derivation of (3.6) directly from (2.7) and (2.9) which is not without interest.…”

Section: The Class Of Uncorrelated Residual Transformationssupporting

confidence: 65%

Invariance Properties of Uncorrelated Residual Transformations

Godolphin

Tullio

1978

Journal of the Royal Statistical Society Series B: Statistical Methodology

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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 uncorrelated residuals satisfying a given partitioning of the design matrix is derived. It is also shown that each member of this set enjoys an additional invariance property which enables it to be expressed as the same transformation of the vectors of observations, disturbances or least‐squares residuals. Several implications of the results are discussed.

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Section: The Class Of Uncorrelated Residual Transformationssupporting

confidence: 65%

Invariance Properties of Uncorrelated Residual Transformations

Godolphin

Tullio

1978

Journal of the Royal Statistical Society Series B: Statistical Methodology

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“…When testing against heteroskedasticity, choose the middle k observations; when testing against first-order autocorrelation, choose the first k observations or the last k or a mixture of the two. Improvements and extensions of Theil's work on BLUS residuals can be found in Koerts (1967), Putter (1967), Koerts and Abrahamse (1968), Abrahamse and Koerts (1971) and others.…”

Section: Definition 1: Consider the Linear Regression Model Ymentioning

confidence: 99%

On Theil's errors

Magnus

Sinha

2005

The Econometrics Journal

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“…In [2] such a typical matrix x, say, was adopted for the economic time-series case. It appeared that by using the new residual vector, based on 8, the greater part of the power lost is regained.…”

Section: Some Lossof Quality Must Be Expected Since An Extra Restrictmentioning

confidence: 99%