Groupe d’études et de recherche en analyse des décisions

Empirical Likelihood Approach to Calibration with Survey Data

Changbao Wu

Construction of traditional calibration estimators involves a distance measure between the calibrated weights and the basic design weights and a set of benchmark constraints. The pseudo empirical likelihood (PEL) method can achieve the same goal of calibration as well as enjoy several attractive features. These include (i) likelihood based motivations; (ii) intrinsic positive weights for the maximum PEL estimators; (iii) availability of PEL ratio confidence intervals; and (iv) flexibility in combining information from multiple surveys and multi-frame surveys. In this talk I will provide an overview on some recent development of the PEL method in survey sampling and discuss its relation to the calibration method. The PEL approach requires that the population means of auxiliary variables be known while the general calibration method assumes that the population totals of auxiliary variables are available, and there is a gap between the two approaches when the population size N is unknown. This gap can be bridged by using the minimum entropy distance which is closely related to the PEL function. Major features of the PEL approach are highlighted and several related issues, including computational algorithms, are addressed. (Joint work with J.N.K. Rao)