Some Bayesian and Non-Bayesian Procedures for the Analysis of Comparative Experiments and for Small-Area Estimation: Computational Aspects, Frequentist Properties, and Relationships

Hulting, Frederick L.; Harville, David A.

doi:10.1080/01621459.1991.10475080

Cited by 30 publications

(11 citation statements)

References 50 publications

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“…The poor performance of the MSE approximations when the variance ratio is close to 0 is not unique to our study and has been noted in other studies. As discussed by Hulting and Harville (1991), when ! 1 a!…”

Section: Prefacementioning

confidence: 96%

“…Following Hulting and Harville (1991), we viewed the MSE b approximations as also approximating the MSE f of the EBLUP and studied their frequentist properties. Hence, we considered eight MSE approximations in the simulation study: the naõÈ ve, Kackar and Harville (1984), Prasad and Rao (1990), MCPR, KS-I, KS-II*, MC and MMC.…”

Section: Computation Of Mse F and Mse B Approximations And Evaluationmentioning

confidence: 99%

“…Under model (1.1), the means yip include both ®xed and random eects and hence they can be predicted very naturally under both the frequentist and the Bayesian approaches. Empirically, it is often found that the two approaches lead to similar predictors and prediction MSEs; see, for example, Hulting and Harville (1991) and Ghosh and Rao (1994). The main purpose of this paper is to study and test this empirical ®nding analytically with some added empirical results.…”

Section: Introductionmentioning

confidence: 97%

“…In Section 6, ®nite sample frequentist properties of the eight methods (naõÈ ve, Kackar and Harville (1984), Prasad and Rao (1990), MCPR, KS-I, KS-II*, MC and MMC) of approximating the prediction MSE are studied by simulations based on real data on county crop areas as reported by Battese et al (1988). As illustrated by Hulting and Harville (1991) and Kass and Steey (1989), there are several theoretical results suggesting that the use of Bayesian predictors and the associated posterior variances may be appropriate under frequentist theory. The major conclusions of our study are that the second-order corrections generally reverse the negative bias of the ®rst-order approximations to a positive bias which is much smaller in absolute value, and hence they improve the con®dence interval coverage of the small area means.…”

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Bayesian Versus Frequentist Measures of Error in Small Area Estimation

Singh

Stukel

Pfeffermann

1998

Journal of the Royal Statistical Society Series B: Statistical Methodology

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This paper compares analytically and empirically the frequentist and Bayesian measures of error in small area estimation. The model postulated is the nested error regression model which allows for random small area effects to represent the joint effect of small area characteristics that are not accounted for by the ®xed regressor variables. When the variance components are known, then, under a uniform prior for the regression coef®cients and normality of the error terms, the frequentist and the Bayesian approaches yield the same predictors and prediction mean-squared errors (MSEs) (de®ned accordingly). When the variance components are unknown, it is common practice to replace the unknown variances by sample estimates in the expressions for the optimal predictors, so that the resulting empirical predictors remain the same under the two approaches. The use of this paradigm requires, however, modi®cations to the expressions of the prediction MSE to account for the extra variability induced by the need to estimate the variance components. The main focus of this paper is to review and compare the modi®cations to prediction MSEs proposed in the literature under the two approaches, with special emphasis on the orders of the bias of the resulting approximations to the true MSEs. Some new approximations based on Monte Carlo simulation are also proposed and compared with the existing methods. The advantage of these approximations is their simplicity and generality. Finite sample frequentist properties of the various methods are explored by a simulation study. The main conclusions of this study are that the use of second-order bias corrections generally yields better results in terms of the bias of the MSE approximations and the coverage properties of con®dence intervals for the small area means. The Bayesian methods are found to have good frequentist properties, but they can be inferior to the frequentist methods. The second-order approximations under both approaches have, however, larger variances than the corresponding ®rst-order approximations which in most cases result in higher MSEs of the MSE approximations.

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Section: Prefacementioning

confidence: 96%

Section: Computation Of Mse F and Mse B Approximations And Evaluationmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 97%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Bayesian Versus Frequentist Measures of Error in Small Area Estimation

Singh

Stukel

Pfeffermann

1998

Journal of the Royal Statistical Society Series B: Statistical Methodology

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show abstract

“…Hence, the behavior of an individual is quite strongly related between the last two states but only loosely related between the first two states. A 95% prediction interval (Hulting and Harville, 1991) was computed to check whether the influence of the predicted random effect for each state is significant:…”

Section: Application To Corsican Pine Growthmentioning

confidence: 99%

Markov and Semi‐Markov Switching Linear Mixed Models Used to Identify Forest Tree Growth Components

Chaubert-Pereira¹,

Guédon²,

Lavergne³

et al. 2009

Biometrics

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Modelling covariance structure in the analysis of repeated measures data

2000

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The term ‘repeated measures’ refers to data with multiple observations on the same sampling unit. In most cases, the multiple observations are taken over time, but they could be over space. It is usually plausible to assume that observations on the same unit are correlated. Hence, statistical analysis of repeated measures data must address the issue of covariation between measures on the same unit. Until recently, analysis techniques available in computer software only offered the user limited and inadequate choices. One choice was to ignore covariance structure and make invalid assumptions. Another was to avoid the covariance structure issue by analysing transformed data or making adjustments to otherwise inadequate analyses. Ignoring covariance structure may result in erroneous inference, and avoiding it may result in inefficient inference. Recently available mixed model methodology permits the covariance structure to be incorporated into the statistical model. The MIXED procedure of the SAS® System provides a rich selection of covariance structures through the RANDOM and REPEATED statements. Modelling the covariance structure is a major hurdle in the use of PROC MIXED. However, once the covariance structure is modelled, inference about fixed effects proceeds essentially as when using PROC GLM. An example from the pharmaceutical industry is used to illustrate how to choose a covariance structure. The example also illustrates the effects of choice of covariance structure on tests and estimates of fixed effects. In many situations, estimates of linear combinations are invariant with respect to covariance structure, yet standard errors of the estimates may still depend on the covariance structure. Copyright © 2000 John Wiley & Sons, Ltd.

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Some Bayesian and Non-Bayesian Procedures for the Analysis of Comparative Experiments and for Small-Area Estimation: Computational Aspects, Frequentist Properties, and Relationships

Cited by 30 publications

References 50 publications

Bayesian Versus Frequentist Measures of Error in Small Area Estimation

Bayesian Versus Frequentist Measures of Error in Small Area Estimation

Markov and Semi‐Markov Switching Linear Mixed Models Used to Identify Forest Tree Growth Components

Modelling covariance structure in the analysis of repeated measures data

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