Estimation of population column proportions of 1’s in survey type designs

Abstract

Motivated by the nature of observed responses in real world situations, we propose an iterative algorithm for estimating population column proportions of a n × k Bernoulli random matrix (X) in survey type designs. The Perron-Frobenius theorem is used to establish the limiting form of the proposed estimator in the iteration process, where pj , is given by the row sum of the Perron projection of XtX or An asymptotic distribution of the proposed estimator is provided in this paper.