Bayes linear estimation for finite population with emphasis on categorical data

Bayes linear estimator for finite population is obtained from a two-stage regression model, specified only by the means and variances of some model parameters associated with each stage of the hierarchy. Many common design-based estimators found in the literature can be obtained as particular cases. A new ratio estimator is also proposed for the practical situation in which auxiliary information is available. The same Bayes linear approach is proposed for obtaining estimation of proportions for multiple categorical data associated with finite population units, which is the main contribution of this work. A numerical example is provided to illustrate it.