Calibration Estimators by Penalty Function Method

Abstract

Estimation of finite population total using calibration has been considered by several authors. A distance measure is minimized subject to some calibration constraints, usually by way of introducing langrage equation whose solution gives the design weights used in estimation of population total. Sometimes a solution to the langrage constants does not exist. In this paper, we have considered the calibration problem as a nonlinear constrained minimization problem, which we transform to an unconstrained optimization problem using penalty functions. The design weights are obtained iteratively in a numerical manner.  We show that the resulting estimator is more accurate than the popular Horvitz Thompson design estimator

Keywords: calibration, interior penalty function, exterior penalty function