Availability of survey data allows users to obtain estimates for a whole variety of subpopulations, called small areas, obviously not restricted to the planned domains. Often the sample sizes for such domains are too small to provide sufficiently accurate design-based estimate of the domain parameters. To improve such estimates, indirect estimators introduce a linking model that relies on auxiliary information to connect small areas thus borrowing strength and increasing the effective sample size. This contribution focuses on area level models, that rely on aggregated, area-specific, quantities and allow to take into account the sampling design through the direct survey estimates and their corresponding (design-based) variance estimates. The most popular area-level model is the Fay-Herriot model, a mixed effects linear regression model with normal random components. In the Fay-Herriot setup, accuracy and precision of small area predictors depend on the validity of the model. Two major underlying assumptions of the Fay-Herriot model are investigated in this contribution, namely the normality of random effects and the assumption of known sampling variances. While the distributional assumption on the sampling errors may be justified by the properties of the direct estimators, the normality assumption for the random effects has no justification other than computational convenience and is difficult to detect in practice, since it involves unobservable quantities. In applications, examples abund of skewed distributions, overdispersion, multimodalities, outliers. For identifiability the Fay Herriot model prescribes known sampling variances, but in practice these quantities are estimated from the sample and then treated as known, with the consequence that inferences neglect the associated uncertainty. We extend the Fay Herriot model within a Bayesian approach in two directions. First, uncertainty on variances is introduced in the model, so as to reflect the fact that they are actually estimated from survey data. Assuming that (independent) information is available about sampling variances, we specify a common distribution generating the variance parameters (Dass et al., 2012). Second, a Bayesian semi- parametric approach is pursued: the default normality assumption for random effects is replaced by a nonparametric specification, namely using a Dirichlet process (Ferguson, 1973; Antoniak, 1974).
A semi-parametric FayHerriot-type model with unknown sampling variances / Polettini, Silvia. - ELETTRONICO. - (2016), pp. 1067-1072. ((Intervento presentato al convegno CLADAG 2015 10th Scientific Meeting of the Classification and Data Analysis Group of the Italian Statistical Society tenutosi a Santa Margherita di Pula (CA), Italy nel October 8-10, 2015.
|Titolo:||A semi-parametric FayHerriot-type model with unknown sampling variances|
|Data di pubblicazione:||2016|
|Citazione:||A semi-parametric FayHerriot-type model with unknown sampling variances / Polettini, Silvia. - ELETTRONICO. - (2016), pp. 1067-1072. ((Intervento presentato al convegno CLADAG 2015 10th Scientific Meeting of the Classification and Data Analysis Group of the Italian Statistical Society tenutosi a Santa Margherita di Pula (CA), Italy nel October 8-10, 2015.|
|Appartiene alla tipologia:||04b Atto di convegno in volume|