M-quantile regression models have recently gained much attention in small area estimation representing a robust and flexible alternative to the widespread use of random effects models. However, since quantiles, and more generally M-quantiles, are only uniquely defined for continuous variables, M-quantile models have been applied up to now only when the variable of interest is continuous. We propose a new approach to small area estimation for count data based on a Poisson-like M-quantile model. Parameter estimates are obtained by suitably extending a robust version of estimating equations for generalized linear models to handle M-quantile regression. A measure of accuracy of the proposed small area estimators is provided that uses nonparametric bootstrap. The proposed methodology is compared with classical small area estimation methods based on generalized linear mixed models via simulation studies. The study is motivated by the need to obtain estimates from the Italian National survey on Health Conditions and Appeal to Medicare for the average number of visits to physicians. Small area estimation techniques are needed because the survey is designed to provide reliable estimates at the level of Administrative Regions - NUTS2 level – while estimates are sought at the level of Health Districts (partition of the Administrative Regions).
Small area estimates of counts using M-quantile Poisson regression models
RANALLI, Maria Giovanna;
2012
Abstract
M-quantile regression models have recently gained much attention in small area estimation representing a robust and flexible alternative to the widespread use of random effects models. However, since quantiles, and more generally M-quantiles, are only uniquely defined for continuous variables, M-quantile models have been applied up to now only when the variable of interest is continuous. We propose a new approach to small area estimation for count data based on a Poisson-like M-quantile model. Parameter estimates are obtained by suitably extending a robust version of estimating equations for generalized linear models to handle M-quantile regression. A measure of accuracy of the proposed small area estimators is provided that uses nonparametric bootstrap. The proposed methodology is compared with classical small area estimation methods based on generalized linear mixed models via simulation studies. The study is motivated by the need to obtain estimates from the Italian National survey on Health Conditions and Appeal to Medicare for the average number of visits to physicians. Small area estimation techniques are needed because the survey is designed to provide reliable estimates at the level of Administrative Regions - NUTS2 level – while estimates are sought at the level of Health Districts (partition of the Administrative Regions).I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
