Modelo de regressão quantílica bayesiano para estimação em pequenos domínios a nível de unidade

Abstract

In this dissertation, we present a new class of models for small area estimation at the unit level. Small areas (or small domains) are groups for which the observed sample is too small and, therefore, not representative. The study of estimation in small domains is extremely important due to its connection with policy-making, allocation of public funds, planning, among other applications, requiring increasingly accurate statistics. The proposed model shares the general structure of traditional unit-level models—comprising a component that incorporates covariate effects and another with area-specific random effects. However, unlike standard quantile regression, this model allows both covariate effects and random effects to vary across quantiles.The model is developed within a Bayesian framework and assumes that the variable of interest follows an asymmetric Laplace distribution, regardless of the true distribution of the data. The use of an exponential-normal mixture representation enables the derivation of closed-form full conditional distributions. The goal of this project is to introduce the quantile regression approach into the context of small area estimation from a Bayesian perspective. As a result, the proposed model enables analysis not only at central tendency measures, such as the mean, but also at any desired quantile. The proposed model and predictive alternatives were evaluated using bias, mean squared error (MSE), and mean absolute error (MAE), and compared to commonly used models in the literature.