Horvitz-Thompson Estimators in Center Sampling.

The problem of the estimation of the size of an immigrant population is very important in many countries as well as in Italy. Center sampling theory has been recently proposed and it is based on the hypothesis that all the individuals use to frequent centers of aggregation. Two approaches to center sampling are developed in literature. In the first people are drawn through simple random sampling without replacement from all the availables centers. In the second one centers are drawn through the same scheme and all the individuals in the sample centers are considered. In this paper the second approach is followed and generalized to a different sampling scheme according to the situation in which all centers has not the same importance: i.e. a big center could have a higher selection probability than a little center. So an unequal selection probablilities scheme is presented