QUASI-LINEAR BAYES ESTIMATION IN STRATIFIED FINITE POPULATIONS

In this paper a Bayesian least squares approximation is proposed for d escriptive inference in a finite population when a categorical auxilia ry variable is known. A hierarchical model II analysis of variance is assumed. The solution consists of a projection on the vector of group totals and on the between and within sums of squares. The approximatio n can be seen as a normal approximation of the joint distribution of t he statistic and of the parameter of interest, conditional on two disc rete variables: these denote attribution to one group and selection in the sample. The main consequence of the conditioning is that conjectu res about non-normality can be taken into account. The solution is com pared with others that have been published.