The General Multivariate Gauss—Markov Model of the Incomplete Block Design

Oktaba, Wiktor

doi:10.1111/1467-842x.00275

Cited by 3 publications

(2 citation statements)

References 10 publications

(12 reference statements)

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“…As recalled by Oktaba (2003), methods of linear statistical inference are related to the Gauss−Markov model, originally considered by Gauss (1809Gauss ( , 1855 and Markov (1900) in a simple form, later extended and studied by many prominent statisticians (see also Rao, 1971, Section 1.1). One of the generalizations of particular interest is the so-called general uni-and multivariate Gauss−Markov model on which the analyses of experiments are based.…”

Section: Introductionmentioning

confidence: 99%

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On the General Gauss-Markov Model for Experiments in Block Designs

Caliński

2012

Biometrical Letters

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SummaryThe main estimation and hypothesis testing results related to the Gauss− Markov model, in its general form, are recalled and the application of these results to the analysis of experiments in block designs is considered. Special attention is given to the randomization-derived model for a general block design, and for a proper block design in particular. The question whether the randomization-derived model can be considered as a particular general Gauss−Markov model is discussed. It is indicated that the former, as a mixed model, is in fact an extension of the general Gauss−Markov model. Thus, the analysis based on the randomization-derived model requires a more extended methodical approach. The present paper has been inspired by one of the last papers of Professor Wiktor Oktaba.

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Section: Introductionmentioning

confidence: 99%

“…To simplify the considerations, from now on only the so-called proper block designs (i.e., such for which Oktaba (2003), will be taken into account.…”

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confidence: 99%

On the General Gauss-Markov Model for Experiments in Block Designs

Caliński

2012

Biometrical Letters

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On equivalence of predictors/estimators under a multivariate general linear model with augmentation

Jiang

Tian

2017

Journal of the Korean Statistical Society

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A study of the equivalence of inference results in the contexts of true and misspecified multivariate general linear models

Yuan

Jiang

Tian

2023

MATH

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<abstract><p>In practical applications of regression models, we may meet with the situation where a true model is misspecified in some other forms due to certain unforeseeable reasons, so that estimation and statistical inference results obtained under the true and misspecified regression models are not necessarily the same, and therefore, it is necessary to compare these results and to establish certain links between them for the purpose of reasonably explaining and utilizing the misspecified regression models. In this paper, we propose and investigate some comparison and equivalence analysis problems on estimations and predictions under true and misspecified multivariate general linear models. We first give the derivations and presentations of the best linear unbiased predictors (BLUPs) and the best linear unbiased estimators (BLUEs) of unknown parametric matrices under a true multivariate general linear model and its misspecified form. We then derive a variety of necessary and sufficient conditions for the BLUPs/BLUEs under the two competing models to be equal using a series of highly-selective formulas and facts associated with ranks, ranges and generalized inverses of matrices, as well as block matrix operations.</p></abstract>

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The General Multivariate Gauss—Markov Model of the Incomplete Block Design

Cited by 3 publications

References 10 publications

On the General Gauss-Markov Model for Experiments in Block Designs

On the General Gauss-Markov Model for Experiments in Block Designs

On equivalence of predictors/estimators under a multivariate general linear model with augmentation

A study of the equivalence of inference results in the contexts of true and misspecified multivariate general linear models

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