A Two-Part Geoadditive Small Area Model for Geographical Domain Estimation

We are interested in estimating small domain means of a response variable that shows a spatial trend and has a continuous skewed distribution with a large number of values clustered at zero. This kind of variable can occur in many surveys, like business or agricultural surveys: examples are the quantity of crops produced or the amount of land allocated for their production collected by the Farm Structure Survey driven by the Italian Statistical Institute. The small sample size within the areas requires the use of small area model dependent methods to increase the effective area sample size by using census and administrative auxiliary data. To account simultaneously for the excess of zeros, the skewness of the distribution and the possible spatial trend of the data, we present a two-part geoadditive small area model. An application to the estimation of the per-farm average grapevine production in Tuscany at Agrarian Region level shows the satisfactory performance of the model.