Two New Functional Forms of Calibration Constraints

Abstract

The calibration approach is widely used to estimate the population parameters of study variable when the population total(s) of the auxiliary variable(s) are known. This approach encounters two major problems: firstly, of extreme and negative weights and secondly regarding convergence. Convergence of calibration weights is a serious issue in the estimation of population parameters when multiple auxiliary variables are involved. The calibration weights have to satisfy a large number of constraints; this may cause them not to converge to a specified range. In this article, a novel approach is presented to overcome the problem of convergence of calibration weights. Furthermore, a simple form of weighted calibration-constraints is proposed to avoid the unwanted effects of auxiliary variables used in the estimation procedure. The proposed approach is different from previously considered ridge regression approach as auxiliary variables are controlled exogenously by using a control matrix, instead of adding a penalty term in the diagonal elements of variance covariance matrix.