Matrix algebra and sampling theory: The case of the Horvitz-Thompson estimator

Matrix algebra is a tool not commonly employed in sampling theory. The intention of this paper is to help change this situation by showing, in the context of the Horvitz-Thompson (HT) estimator, the convenience of the use of a number of matrix-algebra results. Sufficient conditions for the consistency and the rate of convergence of the HT estimator are given. These conditions are based on matrix inequalities that are employed to bound the variance of the HT estimator.