The effect of Informative Selection on the estimation of parameters related to Spatial Processes

Abstract

This paper extends the concept of informative selection, population distribution and sample distribution to a spatial process context. These notions were first defined in a context where the output of the random process of interest consists of independent and identically distributed realisations for each individual of a population. It has been showed that informative selection was inducing a stochastic dependence among realisations on the selected units. In the context of spatial processes, the "population" is a continuous space and realisations for two different elements of the population are not independent. We show how informative selection may induce a different dependence among selected units and how the sample distribution differs from the population distribution.