A Comparison of Two Criteria for Ordinary-Least-Squares Estimators to Be Best Linear Unbiased Estimators

Baksalary, Jerzy K.; Eijnsbergen, A.C. van

doi:10.1080/00031305.1988.10475567

Cited by 9 publications

(3 citation statements)

References 12 publications

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“…However it is important at the outset to distinguish two cases. Baksalary & van Eijnsbergen (1988) provide a careful review of some of the confusions that have a risen in the literature on conditions for OLSE to be BLUE. Their remarks also apply to BLUE 1 ⊂ BLUE 2 .…”

Section: General Conditions For Blue 1 ⊂ Bluementioning

confidence: 99%

“…There are complications, even in this comparatively simple case, as the literature itself has occasionally become slightly confused. For example, Baksalary & van Eijnsbergen (1988) point out that the generality of a seminal paper by McElroy (1967) has been misquoted by Searle (1971, p. 89), Odell (1983) and by Milliken & Albohali (1984). There are certainly theoretical issues behind the "equivalence" question even for the linear model; these explain the treatment of authors such as Puntanen & Styan (1989), Mathew (1983) and Rao (1967Rao ( , 1968Rao ( , 1971) but there are practical issues as well.…”

Section: Introductionmentioning

confidence: 99%

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A Review of Conditions Under Which Blues and/or Blups in One Linear Mixed Model are also Blues and/or Blups in Another

Haslett

Puntanen

2013

Calcutta Statistical Association Bulletin

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Abtsrcat The linear mixed model, with its combination of fixed and random parameters, plays a central role in many statistical applications. Here we review results on conditions for best linear unbiased estimates (BLUEs) of estimable functions of fixed parameters under one linear mixed model to remain BLUEs under a second model, which difiers from the first in covariance structure. Without making full rank assumptions for design matrices or covariance matrices, we also review results for the conditions under which best linear unbiased predictors (BLUPs) of random parameters under the first model remain BLUPs under the second model, and for the conditions under which both BLUEs and BLUPs under the first model remain the BLUEs and BLUPs under the second. We also provide a rather generous list of related references.

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Section: General Conditions For Blue 1 ⊂ Bluementioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

A Review of Conditions Under Which Blues and/or Blups in One Linear Mixed Model are also Blues and/or Blups in Another

Haslett

Puntanen

2013

Calcutta Statistical Association Bulletin

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“…Balestra (1970) claims that this result is clear enough to not require proof. And the main survey articles, Baksalary and Eijnsbergen (1988) and Puntanen and Styan (1989), ignore this case altogether except for a one-variable result by Watson (1967). Zyskind's (1969) condition, ¼ aI, states that no form of dependence is permissible in the errors when a constant term is not included.…”

Section: Summary Of Necessary and Sufficient Conditions For The Clrm mentioning

confidence: 99%

Reconciling Conflicting Gauss-Markov Conditions in the Classical Linear Regression Model

Larocca¹

2005

Polit. anal.

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This article reconciles conflicting accounts of Gauss-Markov conditions, which specify when ordinary least squares (OLS) estimators are also best linear unbiased (BLU) estimators. We show that exogeneity constraints that are commonly assumed in econometric treatments of the Gauss-Markov theorem are unnecessary for OLS estimates of the classical linear regression model to be BLU. We also generalize a set of necessary and sufficient conditions first established by McElroy (1967, Journal of the American Statistical Association 62:1302–1304), but not yet generally recognized in the econometric literature, that are appropriate for many political science applications. McElroy's conditions relax the traditional Gauss-Markov restriction on autocorrelation in the errors to allow a type of correlation, exchangeability, that has two desirable characteristics: (1) exchangeable data occur in a potentially important class of political science models, and (2) the form of autocorrelation that occurs in exchangeable data has a ready intuition. We thus show that a common class of sample selection models that does not satisfy the Gauss-Markov conditions specified in econometrics textbooks is, in fact, BLU under OLS estimation.

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The Legend of the Equality of OLSE and BLUE: Highlighted by C. R. Rao in 1967

Markiewicz

Puntanen

Styan

2021

Methodology and Applications of Statistics

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A Comparison of Two Criteria for Ordinary-Least-Squares Estimators to Be Best Linear Unbiased Estimators

Cited by 9 publications

References 12 publications

A Review of Conditions Under Which Blues and/or Blups in One Linear Mixed Model are also Blues and/or Blups in Another

A Review of Conditions Under Which Blues and/or Blups in One Linear Mixed Model are also Blues and/or Blups in Another

Reconciling Conflicting Gauss-Markov Conditions in the Classical Linear Regression Model

The Legend of the Equality of OLSE and BLUE: Highlighted by C. R. Rao in 1967

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