Calibration estimation of distribution function based on multidimensional scaling of auxiliary information

Abstract

The distribution function is a functional parameter of great interest in many research areas, such as medicine or economics. Among other properties, it facilitates the estimation of parameters such as quantiles. Accordingly, techniques are needed to estimate this function efficiently. Survey statisticians have access to large, high-dimension databases and use them to optimise the estimates obtained. One way to incorporate auxiliary information in the estimation stage is through the calibration method, which was initially designed to estimate totals and means and consists of adjusting new sample weights in order to reduce the variance of estimators. However, calibration techniques may be subject to over-calibration, i.e. the loss of efficiency when high-dimension auxiliary data sets are incorporated. Although alternative approaches have been proposed, in which the calibration method incorporates auxiliary information in the estimation of the distribution function, these alternatives do not seek to incorporate qualitative auxiliary information, which must be introduced in the usual way through dummy variables. However, this workaround can greatly increase the dimension of the auxiliary information, producing either over-calibration or even incompatible calibration constraints. In this article, we propose adapting the calibration method through multidimensional scaling, in order to incorporate quantitative and qualitative information, thus avoiding the negative consequences of over-calibration in the estimation of the distribution function.