A note on equality of MINQUE and simple estimator in the general Gauss-Markov model

Groβ, Jürgen

doi:10.1016/s0167-7152(97)00030-8

Cited by 6 publications

(7 citation statements)

References 10 publications

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“…The latter result was generalized by Kurata (1998). See also Groß (1997). In this paper, we generalize their result by considering the case in whicĥ…”

Section: Introductionmentioning

confidence: 63%

Covariance structure associated with an equality between two general ridge estimators

Tsukuda

Kurata

2017

Stat Papers

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In a general linear model, this paper derives a necessary and sufficient condition under which two general ridge estimators coincide with each other. The condition is given as a structure of the dispersion matrix of the error term. Since the class of estimators considered here contains linear unbiased estimators such as the ordinary least squares estimator and the best linear unbiased estimator, our result can be viewed as a generalization of the well-known theorems on the equality between these two estimators, which have been fully studied in the literature. Two related problems are also considered: equality between two residual sums of squares, and classification of dispersion matrices by a perturbation approach.

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“…The latter result was generalized by Kurata (1998). See also Groß (1997). In this paper, we generalize their result by considering the case in whicĥ…”

Section: Introductionmentioning

confidence: 63%

Covariance structure associated with an equality between two general ridge estimators

Tsukuda

Kurata

2017

Stat Papers

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“…The equivalences of (i) and (ii) in Theorem 2.2(a) and (b) were given by Groß [1]. Theorem 2.2 shows that under the conditions in (ii) and (iii), we can use the SE instead of the MINQUE, while the SE has the same optimal statistical properties as the MINQUE.…”

Section: Equality For the Se And Minque In The Original Modelmentioning

confidence: 89%

“…If the random vector y in (1.1) is normally distributed, then SE M (σ 2 ) has χ 2 (f )-distribution if and only if E X E X = E X , see Rao and Mitra [6]. More discussion on the distributions of SE M (σ 2 ) and MINQUE M (σ 2 ) can be found in Groß [1]. Also note from (2.1) and (2.2) that the SE of the variance component σ 2 involves no , but does the MINQUE.…”

Section: Equality For the Se And Minque In The Original Modelmentioning

confidence: 99%

“…This topic was also considered in the literature. For example, Groß [1] gave necessary and sufficient conditions for the SE and MINQUE of σ 2 in (1.1) to equal; Wang et al [11] compared the SE and MINQUE of σ 2 in (1.1) through the MSEs of the estimators; Zhang [12] gave some necessary and sufficient conditions for the MINQUEs of σ 2 in (1.1) and (1.4) to equal. The purpose of this paper is to derive identifying conditions for the SEs and MINQUEs of the variance component σ 2 in (1.1), (1.3) and (1.4) to equal.…”

Section: Introductionmentioning

confidence: 99%

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Some equalities for estimations of variance components in a general linear model and its restricted and transformed models

Tian

Liu

2010

Journal of Multivariate Analysis

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a b s t r a c t For the unknown positive parameter σ 2 in a general linear model M = {y, Xβ, σ 2 }, the two commonly used estimations are the simple estimator (SE) and the minimum norm quadratic unbiased estimator (MINQUE). In this paper, we derive necessary and sufficient conditions for the equivalence of the SEs and MINQUEs of the variance component σ 2 in the original model M , the restricted model M r = {y, Xβ | Aβ = b, σ 2 }, the transformed model M t = {Ay, AXβ, σ 2 A A }, and the misspecified model M m = {y, X 0 β, σ 2 0 }.

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“…Some authors studied statistical properties of σ 2 s when V has some special structures, see, for example, [2,4]. Groß [3] established some necessary and sufficient conditions for the equality σ 2 m = σ 2 s when X and V can be deficient in rank, without the normality assumption of error distribution. The object of the present note is to make further comparison of these two estimates.…”

Section: Introductionmentioning

confidence: 99%

Comparison of MINQUE and Simple Estimate of the Error Variance in the General Linear Models

Wang

Wahab

2003

Acta Mathematicae Applicatae Sinica, English Series

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Comparison is made between the MINQUE and simple estimate of the error variance in the normal linear model under the mean square errors criterion, where the model matrix need not have full rank and the dispersion matrix can be singular. Our results show that any one of both estimates cannot be always superior to the other. Some sufficient criteria for any one of them to be better than the other are established. Some interesting relations between these two estimates are also given.

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A note on equality of MINQUE and simple estimator in the general Gauss-Markov model

Cited by 6 publications

References 10 publications

Covariance structure associated with an equality between two general ridge estimators

Covariance structure associated with an equality between two general ridge estimators

Some equalities for estimations of variance components in a general linear model and its restricted and transformed models

Comparison of MINQUE and Simple Estimate of the Error Variance in the General Linear Models

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