Mean Square Efficiency of Estimators of Variance Components

Klotz, Jerome; Milton, Roy C.; Zacks, Shelemyahu

doi:10.1080/01621459.1969.10501064

Cited by 82 publications

(25 citation statements)

References 9 publications

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“…The proof follows a method suggested by Stein [7], and the main theorem is therefore called Stein's theorem. This theorem has been proven previously in the paper of Klotz, Milton and Zacks [4] with only a slightly different notation. It is reproduced here for the sake of continuity and due to its elegance.…”

Section: The Inadmissibility Of the Bayes Equivariant Estimatorsmentioning

confidence: 55%

“…This in itself is an interesting theoretical result, the establishment of which requires a judicious application of a method introduced previously by Stein [7]. As shown by Klotz, Milton and Zacks in [4], the performance of certain equivariant estimators of a~ is very close to optimal, although the estimators are inadmissible in the general class. Roughly speaking, the inadmissibility of the equivariant estimators is due to the fact that they are all independent of the sample grand mean Y...…”

Section: Introductionmentioning

confidence: 85%

“…We do not have a proof of either admissibility or inadmissibility of these estimators. Numerical comparison of their mean-square-error functions to those of some commonly used equivariant estimators (see [4]) shows that Tiao and Tan's estimators and Stone and Springer's are quite inefficient. The proper Bayes equivariant estimators (3.7) and (3.9) are at least admissible in the class of equivariant estimators.…”

Section: I(j--1)-3 I~(r)(i/2 (I(j--1)-1)/2) Jmentioning

confidence: 98%

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Bayes equivariant estimators of variance components

Zacks

1970

Ann Inst Stat Math

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Section: The Inadmissibility Of the Bayes Equivariant Estimatorsmentioning

confidence: 55%

Section: Introductionmentioning

confidence: 85%

Section: I(j--1)-3 I~(r)(i/2 (I(j--1)-1)/2) Jmentioning

confidence: 98%

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Bayes equivariant estimators of variance components

Zacks

1970

Ann Inst Stat Math

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“…zouned 3 seek dominating estimators. The earliest work of this type is due to Klotz, Milton and Zacks (1969) for the one-way layout. They show, for example, that the MLE of the "between" variance component (see Herbach (1959)), which is itself a positive part estimator, dominates the UJMVU and, using ideas of Stein (1964), iht it in turn can bc dd~mna.zd.…”

Section: Introductionmentioning

confidence: 99%

Improved Estimation of Variance Components in Mixed Models

Gelfand¹,

Dey²

1990

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“…In which case, one level is nested in the other. Usually, the unit of analysis are the individuals (at a lower level) who are nested in within an aggregate unit (at higher level) (Klotz et al (1969); Li et al (2011)). Multilevel (hierarchical) data structure causes correlation among observations within same clusters (Li et al (2011)).…”

mentioning

confidence: 99%

Evaluating Likelihood Estimation Methods in Multilevel Analysis of Clustered Survey Data

Fagbamigbe¹,

Bakre²

2018

AJAS

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Abstract. (Short Abstract) Public health researchers often lay little or no emphasis on multilevel structure of clustered data and its likelihood estimation techniques. This has led to improper inferences. The aim of this research is to evaluate traditional methods and the different multilevel likelihood estimation procedures so as to compare their computational efficiencies. 352Full Abstract. Introduction: Public health researchers often lay little or no emphasis on multilevel structure of clustered data and its likelihood estimation techniques. This has led to improper inferences. The aim of this research is to evaluate traditional methods and the different multilevel likelihood estimation procedures so as to compare their computational efficiencies.Methodology: We fitted mixed method effect regression model into data on use of modern contraceptive from the Nigeria 2012 National HIV/AIDS and Reproductive Health Survey (NARHS) PLUS II with respondent's characteristics as the independent variables. Also, 600,000 observations was simulated to evaluate the performance of Penalized Quasi-Likelihood (PQL), Non-Adaptive Gaussian Quadrature (NAGQ) and Adaptive Gaussian Quadrature (AGQ) using syntax for Mixed Effects Logit Models (XTMELOGIT) and Generalized Linear Latent and Mixed Models (GLLAMM) in Stata and Generalized Linear Mixed Models (GENLINMIXED) in SPSS.Result: Full Maximum Likelihood (ML) methods had highest likelihood values with lowest standard error and was considered the best model for both two and three levels logistic regression in both the survey and simulated data. PQL procedure was least biased compared to the other multilevel full FL methods. The full likelihood method had the least −2logL, AIC and BIC for the two dataset. Which implies that full likelihood procedure had the best fitted model. Also, current age of the respondents, wealth index, residence, education and religion are significant predictors of modern contraceptive use.Conclusion: Full ML performed better than quasi likelihood method at both two and three levels for both simulated and survey data. However, PQL appeared to be the best considering whether the estimates were biased or not. In terms of computational time, NAGQ with XTMELOGIT syntax was the fastest for two-levels and three levels model. The cluster-level effect is more significant than zonal level effect on modern contraceptive use in Nigeria.Résumé (French) Les chercheurs en santé publique accordent souvent peu ou pas d'importanceà la structure multi-niveau des données en grappes (clusterized) et a ses techniques d'estimation basées sur la vraisemblance. Cela peut conduireà des inférences incorrectes. Le but de cette recherche est d'évaluer les méthodes traditionnelles et les différentes procédures d'estimation de vraisemblance multiniveaux afin de comparer leur efficacité.

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Mean Square Efficiency of Estimators of Variance Components

Cited by 82 publications

References 9 publications

Bayes equivariant estimators of variance components

Bayes equivariant estimators of variance components

Improved Estimation of Variance Components in Mixed Models

Evaluating Likelihood Estimation Methods in Multilevel Analysis of Clustered Survey Data

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