Abstract.
Several features of traditional statistical inference can be strengthened by a proper use of spatial information. Two examples are illustrated. The first one is about finite population inference; the talk deepens the concepts of spatial information, geography and prediction in this context. The presentation illustrates a design based individual predictor and how the well-known geographically weighted regression technique can be seen as a version of the Generalized Regression estimation (GREG), at present a very popular tool in model-assisted design-based inference in finite populations. An estimator for the population total is developed, whose statistical properties are derived. A Monte Carlo simulation study highlights the advantages of the proposal. The second example presents a relatively recent research field, which aims at accounting for space in entropy measures, as a generalization when the spatial location of the events is relevant to the purposes of the analysis. The main limitation is that all indices are computed conditional on a chosen distance. Space is exogenous, therefore the bivariate properties cannot be exploited. The inclusion of spatial components in entropy indices induces to investigate the characteristics of the quantity known as conditional entropy in order to include space as a second dimension in the analysis. This way, previously proposed indices such as the contagion index and the co-occurrence based entropy can be extended to a bivariate context, in a setting where the probabilistic meaning of all components is well defined. As a direct consequence, we also obtain an index satisfying the additivity property, as the global conditional entropy is a sum of local entropy measures.