The Equality of the Ordinary Least Squares Estimator and the Best Linear Unbiased Estimator

Puntanen, Simo; Styan, George P. H.

doi:10.1080/00031305.1989.10475644

Cited by 130 publications

(41 citation statements)

References 46 publications

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“…However, if the observed vector y belongs to intersection of C (X : V 1 ) and C (X : V 2 ), then the common operator G will produce the same estimates. Problem : Here the answer is simply the condition which is the classic condition for the equality of OLSE and BLUE; see Puntanen and Styan (1989). Here comes a question: Suppose that HVM = 0.…”

Section: Consequences Of the Non-uniqueness Of The Blue's Representationmentioning

confidence: 97%

Some notes on linear sufficiency

2015

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In this paper we review some important aspects of the linear sufficiency of statistics Fy and consider the relations of the best linear unbiased estimators of the estimable parametric functions under the linear model A and its counterpart A t obtained by transforming A by the matrix F. Most results obtained appear in literature but often in scattered form. Our aim is provide a concise view of this problem area and discuss some possible misunderstandings.

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Section: Consequences Of the Non-uniqueness Of The Blue's Representationmentioning

confidence: 97%

Some notes on linear sufficiency

2015

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“…There is a lot of literature on the equality of ordinary least squares estimator (OLSE) and the BLUE-since the papers by Anderson (1948), Rao (1967), and Zyskind (1967). An extensive review of this area appears in Puntanen and Styan (1989).…”

Section: Olse Vs Bluementioning

confidence: 98%

Effect of adding regressors on the equality of the BLUEs under two linear models

Haslett¹,

Puntanen²

2010

Journal of Statistical Planning and Inference

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“…Applying Lemma 1 to (6.14) and (6.15) yields the equivalence of (a)-(d). The equivalences of (d)-(f) were given in Puntanen and Styan (1989).…”

Section: Rank/inertia Formulas For Olses' Covariance Matricesmentioning

confidence: 99%

Some equalities and inequalities for covariance matrices of estimators under linear model

Tian

2015

Stat Papers

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Best linear unbiased estimators (BLUEs) of unknown parameters under linear models have minimum covariance matrices in the Löwner partial ordering among all linear unbiased estimators of the unknown parameters. Hence, BLUEs' covariance matrices are usually used as a criterion to compare optimality with other types of estimator. During this work, people often need to establish certain equalities and inequalities for BLUEs' covariance matrices, and use them in statistical inference of regression models. This paper aims at establishing some analytical formulas for calculating ranks and inertias of BLUEs' covariance matrices under general linear model, and using these formulas in the comparison of covariance matrices of BLUEs with other types of estimator. This is in fact a mathematical work, and some new tools in matrix analysis are essentially utilized.

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The Equality of the Ordinary Least Squares Estimator and the Best Linear Unbiased Estimator

Cited by 130 publications

References 46 publications

Some notes on linear sufficiency

Some notes on linear sufficiency

Effect of adding regressors on the equality of the BLUEs under two linear models

Some equalities and inequalities for covariance matrices of estimators under linear model

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