Small area estimation for semicontinuous skewed spatial data: an application to the grape wine production in Tuscany

Abstract

Linear-mixed models are frequently used to obtain model-based estimators in small area estimation (SAE) problems. Such models, however, are not suitable when the target variable exhibits a point mass at zero, a highly skewed distribution of the nonzero values and a strong spatial structure. In this paper, a SAE approach for dealing with such variables is suggested. We propose a two-part random effects SAE model that includes a correlation structure on the area random effects that appears in the two parts and incorporates a bivariate smooth function of the geographical coordinates of units. To account for the skewness of the distribution of the positive values of the response variable, a Gamma model is adopted. To fit the model, to get small area estimates and to evaluate their precision, a hierarchical Bayesian approach is used. The study is motivated by a real SAE problem. We focus on estimation of the per-farm average grape wine production in Tuscany, at subregional level, using the Farm Structure Survey data. Results from this real data application and those obtained by a model-based simulation experiment show a satisfactory performance of the suggested SAE approach.

Keywords: Gamma-mixed model; Geostatistical models; Hierarchical Bayesian models; Penalized splines; Two-part random effects models.