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 p_j, $j=1,\dots ,k,$ is given by the row sum of the Perron projection of X^tX or $X^t(1_n-X).$ An asymptotic distribution of the proposed estimator is provided in this paper.

Keywords:

• Bernoulli random matrix
• eigenvalue and eigenvector
• factor analysis
• iterative algorithm
• Perron-Frobenius theorem
• survey design