Unbiasedness of two-stage estimation and prediction procedures for mixed linear models

Kackar, Raghu N.; Harville, David A.

doi:10.1080/03610928108828108

Cited by 132 publications

(78 citation statements)

References 18 publications

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“…This estimator is the more commonly known as Empirical Best Linear Unbiased Predictor (EBLUP) of y j (Henderson, 1953;Kackar and Harville, 1981;Rao, 2003). Two special cases of this estimator may be noted.…”

Section: Linear Mixed Effects Models For Small Area Estimationmentioning

confidence: 99%

M-quantile models for small area estimation

Chambers¹,

Tzavidis²

2006

Biometrika

178

227

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Small area estimation techniques are employed when sample data are insufficient for acceptably precise direct estimation in domains of interest. These techniques typically rely on regression models that use both covariates and random effects to explain variation between domains. However, such models also depend on strong distributional assumptions, require a formal specification of the random part of the model and do not easily allow for outlier robust inference. We describe a new approach to small area estimation that is based on modelling quantile-like parameters of the conditional distribution of the target variable given the covariates. This avoids the problems associated with specification of random effects, allowing inter-domain differences to be characterized by the variation of area-specific M-quantile coefficients. The proposed approach is easily made robust against outlying data values and can be adapted for estimation of a wide range of area specific parameters, including that of the quantiles of the distribution of the target variable in the different small areas. Results from two simulation studies comparing the performance of the M-quantile modelling approach with more traditional mixed model approaches are also provided. SUMMARYSmall area estimation techniques are employed when sample data are insufficient for acceptably precise direct estimation in domains of interest. These techniques typically rely on regression models that use both covariates and random effects to explain variation between domains. However, such models also depend on strong distributional assumptions, require a formal specification of the random part of the model and do not easily allow for outlier robust inference. We describe a new approach to small area estimation that is based on modelling quantile-like parameters of the conditional distribution of the target variable given the covariates. This avoids the problems associated with specification of random effects, allowing inter-domain differences to be characterized by the variation of area-specific M-quantile coefficients. The proposed approach is easily made robust against outlying data values and can be adapted for estimation of a wide range of area specific parameters, including that of the quantiles of the distribution of the target variable in the different small areas. Results from 2 two simulation studies comparing the performance of the M-quantile modelling approach with more traditional mixed model approaches are also provided.

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Section: Linear Mixed Effects Models For Small Area Estimationmentioning

confidence: 99%

M-quantile models for small area estimation

Chambers¹,

Tzavidis²

2006

Biometrika

178

227

View full text Add to dashboard Cite

show abstract

“…It remains unbiased under some weak assumptions (inter alia symmetric but not necessarily normal distribution of random components for the model assumed for the whole population). The proof is presented byŻadło (2004) for the empirical version of Royall (1976) BLUP and it is based on the results presented by Kackar and Harville (1981) for the empirical version of the BLUP proposed by Henderson (1950). The problem of MSE estimation based on the Taylor expansion is considered in many papers on small area estimation but for the empirical version of BLUP proposed by Henderson (1950).…”

Section: Empirical Best Linear Unbiased Predictormentioning

confidence: 99%

On longitudinal moving average model for prediction of subpopulation total

Żądło

2014

Stat Papers

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In the paper the empirical best linear unbiased predictor of the subpopulation total is proposed under some longitudinal model where both temporal and spatial moving average models of profile specific random components are taken into account. Two estimators of the mean square error of the predictor are proposed as well. Considerations are supported by two Monte Carlo simulation studies and the case study.

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“…Nevertheless if σ 2 and Φ are estimated by maximum likelihood, then a maximum likelihood estimate of α is obtained by substitutingV for V in equation 6, whereV is computed from the ML estimatesσ 2 and Φ. While some of the conditions of Aitken's theorem do no longer hold, the ML estimatê α ML is still unbiased, that is, it equals the true population parameter in expectation (Kackar and Harville, 1981).…”

Section: Why Maximum Likelihood Estimates Of Coe Cients In Multilevelmentioning

confidence: 99%

No Need to Turn Bayesian in Multilevel Analysis with Few Clusters: How Frequentist Methods Provide Unbiased Estimates and Accurate Inference

Elff¹,

Heisig²,

Schaeffer³

et al. 2016

Preprint

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Comparative political science has long worried about the performance of multilevel models when the number of upper-level units is small. Exacerbating these concerns, an inuential Monte Carlo study by Stegmueller (2013) suggests that frequentist methods yield biased estimates and severely anti-conservative inference with small upper-level samples. Stegmueller recommends Bayesian techniques, which he claims to be superior in terms of both bias and inferential accuracy. In this paper, we reassess and refute these results. First, we formally prove that frequentist maximum likelihood estimators of coe cients are unbiased. The apparent bias found by Stegmueller is simply a manifestation of Monte Carlo Error. Second, we show how inferential problems can be overcome by using restricted maximum likelihood estimators for variance parameters and a t-distribution with appropriate degrees of freedom for statistical inference. Thus, accurate multilevel analysis is possible without turning to Bayesian methods, even if the number of upper-level units is small.

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Unbiasedness of two-stage estimation and prediction procedures for mixed linear models

Cited by 132 publications

References 18 publications

M-quantile models for small area estimation

M-quantile models for small area estimation

On longitudinal moving average model for prediction of subpopulation total

No Need to Turn Bayesian in Multilevel Analysis with Few Clusters: How Frequentist Methods Provide Unbiased Estimates and Accurate Inference

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