Robust linear mixed models for Small Area Estimation

Fabrizi, Enrico; Trivisano, Carlo

doi:10.1016/j.jspi.2009.07.022

Cited by 21 publications

(17 citation statements)

References 20 publications

(27 reference statements)

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“…Recently, a number of authors have employed flexible parametric distributions to replace the normality assumption of existing model-based formulations. An early exploration by Fabrizi and Trivisano [119] has been followed by formulations using either univariate SN (Ferraz and Moura [120]) or multivariate SN distributions (Ferrante and Pacei [121]), for so-called area-level models. The work of Diallo and Rao [122] is on unit-level modeling based on the CSN/SUN distribution.…”

Section: Methods For Observational Studies and The Social Sciencesmentioning

confidence: 99%

A Selective Overview of Skew-Elliptical and Related Distributions and of Their Applications

Adcock

Azzalini

2020

Symmetry

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Within the context of flexible parametric families of distributions, much work has been dedicated in recent years to the theme of skew-symmetric distributions, or symmetry-modulated distributions, as we prefer to call them. The present contribution constitutes a review of this area, with special emphasis on multivariate skew-elliptical families, which represent the subset with more immediate impact on applications. After providing background information of the distribution theory aspects, we focus on the aspects more relevant for applied work. The exposition is targeted to non-specialists in this domain, although some general knowledge of probability and multivariate statistics is assumed. Given this aim, the mathematical profile is kept to the minimum required.

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Section: Methods For Observational Studies and The Social Sciencesmentioning

confidence: 99%

A Selective Overview of Skew-Elliptical and Related Distributions and of Their Applications

Adcock

Azzalini

2020

Symmetry

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“…It can be treated as the alternative to the average mean squared error studied, e.g. by Fabrizi and Trivisano (2010 …”

Section: Alternative Prediction Accuracy Measuresmentioning

confidence: 99%

On Asymmetry of Prediction Errors in Small Area Estimation

Żądło

2017

Statistics in Transition New Series

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The mean squared error reflects only the average prediction accuracy while the distribution of squared prediction error is positively skewed. Hence, assessing or comparing accuracy based on the MSE (which is the mean of squared errors) is insufficient and even inadequate because we should be interested not only in the average but in the whole distribution of prediction errors. This is the reason why we propose to use different than MSE measures of prediction accuracy in small area estimation. In the prediction accuracy comparisons we take into account our proposal for the empirical best predictor, which is a generalization of the predictor presented by Molina and Rao (2010). The generalization results from the assumption of a longitudinal model and possible changes of the population and subpopulations in time.

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“…However, consistently with Section we have

{boldb}_{c} \sim MVN false(bold0, σ_{b c}^{2} Ω_{K}^{- 1} false),

when thin plate splines are used—equation —and

{boldw}_{c} \sim MVN false{bold0, σ_{b c}^{2} diag {false(bolds false)}^{- 1} false},

when the Demmler–Reinsch orthogonalization is employed—equation . The normality of the random effects is a standard assumption in hierarchical models including those used in representing splines (Crainiceanu et al ., ); moreover, Fabrizi and Trivisano () proved that posterior distributions of small area means and totals are little sensitive to failures of the assumed normality of the random effects under widely used small area hierarchical models except in extreme and unlikely cases.…”

Section: The Latent Class Small Area Modelmentioning

confidence: 99%

A Hierarchical Latent Class Model for Predicting Disability Small Area Counts from Survey Data

Fabrizi

Montanari

Ranalli

2015

Journal of the Royal Statistical Society Series A: Statistics in Society

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This article considers the estimation of the number of severely disabled people using data from the Italian survey on Health Conditions and Appeal to Medicare. Disability is indirectly measured using a set of categorical items, which survey a set of functions concerning the ability of a person to accomplish everyday tasks. Latent Class Models can be employed to classify the population according to different levels of a latent variable connected with disability. The survey, however, is designed to provide reliable estimates at the level of Administrative Regions (NUTS2 level), while local authorities are interested in quantifying the amount of population that belongs to each latent class at a sub-regional level. Therefore, small area estimation techniques should be used. The challenge of the present application is that the variable of interest is not observed. Adopting a full Bayesian approach, we base small area estimation on a Latent Class model in which the probability of belonging to each latent class changes with covariates and the influence of age is learnt from the data using penalized splines. DeimmlerReisch bases are shown to improve speed and mixing of MCMC chains used to simulate posteriors.

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Robust linear mixed models for Small Area Estimation

Cited by 21 publications

References 20 publications

A Selective Overview of Skew-Elliptical and Related Distributions and of Their Applications

A Selective Overview of Skew-Elliptical and Related Distributions and of Their Applications

On Asymmetry of Prediction Errors in Small Area Estimation

A Hierarchical Latent Class Model for Predicting Disability Small Area Counts from Survey Data

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