Estimators for the One-Way Random Effects Model with Unequal Error Variances

Many finite populations which are sampled repeatedly change slowly over time. Then estimation of finite population characteristics for the current occasion, I, may be improved by the use of data from previous surveys. In this article we investigate the use of empirical Bayes procedures based on two superpopulation models. Each model has the same first stage: The values of the population units on the ith occasion are a random sample from the normal distribution with mean p, and variance U: . At the second stage we assume that either (a) p , . . . . , p, are a random sample from the normal distribution with mean 8 and variance a' , or (b) given a :and 7, p, has the normal distribution with mean 8 and variance U : T (independently for each i), whereas the u: are a random sample from the inverse gamma distribution with parameters 1 / 2 and K/2. In (a) the u : , 8, and 6' are assumed to be unknown, whereas in (b) 8, 7 , and K are unknown. We develop empirical Bayes point estimators and confidence intervals for the finite population mean on the Ith occasion and make large-sample comparisons with the corresponding Bayes estimators and intervals. These are asymptotic results obtained within the framework of "classical" empirical Bayes theory. To complement the asymptotic results we present the results of an extensive numerical investigation of the properties of these estimators and intervals when sample sizes are moderate. The methodology described here is also appropriate for "small area" estimation.

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“…an estimator of ti2, the mean square error (MSE) of 8isR is smaller than that of its competitors (Rao et al 1981).…”

Section: Properties For Moderate Sized Samplesmentioning

confidence: 98%

Empirical Bayes Estimation for the Finite Population Mean on the Current Occasion

Nandram

Sedransk

1993

Journal of the American Statistical Association

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“…Mazodier and Trognon (1978), Baltagi and Griffin (1988) and Roy (2002), etc. consider panel heteroskedasticity models by assuming that Rao et al (1981), Magnus (1982), Baltagi (1988), Wansbeek (1989) and Li and Stengos (1994), etc. assume that μ i ∼ N(0, σ 2 μ ) and v it ∼ N(0, σ 2 v i ).…”

Section: A Random Coefficient Model With Heteroskedasticitymentioning

confidence: 99%

Assessing the contribution of R&D to total factor productivity—a Bayesian approach to account for heterogeneity and heteroskedasticity

Bresson¹,

Hsiao

Pirotte

2011

AStA Adv Stat Anal

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“…Beginning with Cochran (1937), the literature has grown explosively over the last few decades. Among others, we may refer to Iyer, Wang, and Mathew (2004), Paule and Mandel (1982), Rao, Kaplan, and Cochran (1981), Rukhin, Biggerstaff, and Vangel (2000), and Rukhin and Vangel (1998). There is a little work in this problem from the Bayesian viewpoint under the reference prior or matching prior.…”

Section: Introductionmentioning

confidence: 99%

Non-informative priors for the common mean in the one-way random effects model with heterogeneous error variances

Kim

Kang

Joo

2010

Journal of the Korean Statistical Society

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a b s t r a c tThe paper develops some objective priors for the common mean in the one-way random effects model with heterogeneous error variances. We derive the first and second order matching priors and reference priors. It turns out that the second order matching prior matches the alternative coverage probabilities up to the second order, and is also an HPD matching prior. However, derived reference priors just satisfy a first order matching criterion. Our simulation studies indicate that the second order matching prior performs better than the reference prior and the Jeffreys prior in terms of matching the target coverage probabilities in a frequentist sense. We also illustrate our results using real data.

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Estimators for the One-Way Random Effects Model with Unequal Error Variances

Cited by 45 publications

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Empirical Bayes Estimation for the Finite Population Mean on the Current Occasion

Empirical Bayes Estimation for the Finite Population Mean on the Current Occasion

Assessing the contribution of R&D to total factor productivity—a Bayesian approach to account for heterogeneity and heteroskedasticity

Non-informative priors for the common mean in the one-way random effects model with heterogeneous error variances

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