On space sampling designs

Abstract

Statistical research dealing the regional economic problems are based on the spatial data. When spatial populations are large then data about the population elements have to be observed in random samples. In the paper a review of the sampling designs used to draw samples from spatial populations is presented. Especially, the complex sampling designs dependent on auxiliary variables are considered. It is well known that a spatial population should be well covered by the sample. We show that this property is fulfilled by the sampling designs considered in the paper. Moreover, it is mentioned that the sampling designs can be applied to the estimation of the population average in a finite spatial population by means of the well-known Horvitz-Thompson statistic. In general, sampling design proportional to the value of positive function of multidimensional auxiliary variable is considered. It is assumed that all observations of the auxiliary variables are known. Observations of the auxiliary variable can be treated as coordinates of appropriate points in multidimensional space. The sampling designs proportional to the mean of distances between population points and a population centre, to the trace of variance-covariance matrix, to the generalized variance of the auxiliary variable are considered. Some sampling designs proportional to functions of order statistics of the auxiliary variable are presented, too. Finally, the sampling designs dependent on a neighborhood matrix are considered. Sampling schemes implementing the sampling designs are shown, too.