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Title: Estimation of additive parameters under unit-level gamma mixed models Authors:  Tomas Hobza - Czech Technical University in Prague (Czech Republic) [presenting]
Yolanda Marhuenda - Universidad Miguel Hernandez de Elche (Spain)
Domingo Morales - University Miguel Hernandez of Elche (Spain)
Abstract: Average incomes, poverty proportions and poverty gaps are additive parameters obtained as averages of given functions of an income variable. As the variable income has an asymmetric distribution, it is not properly modelled via normal distributions. When dealing with this type of variables, a first option is to apply transformations that approach normality. A second option is to use non-symmetric distributions like the gamma distribution. The use of unit-level gamma mixed models is proposed for modelling positive variables and for deriving three types of predictors of small area additive parameters, called empirical best, marginal and plug-in. The mean squared errors of the predictors are estimated by a parametric bootstrap. Some results of simulation experiments studying the behaviour of the small area predictors and the estimator of the mean squared errors are presented. By using data of the Spanish living condition survey of 2013, an application to the estimation of average incomes and poverty proportions in counties of the region of Valencia is given. In the real data application a procedure for estimating the nuisance parameters is proposed.