A Study on Conditional Likelihood Estimation for Survey Sampling

The pursuit of accurate methods for generalizing attributes of a population from a sampled subset is a problem predating the discipline of statistics. Rather than attempting to characterize a population and so assume that the population perfectly represents its own generative process, a superpopulation approach considers the observed population as a sigma algebra of all possible data generated by a process and is focused upon estimating the parameters of the process rather than producing summary statistics.This study briefly surveys the essentials of survey sampling and evaluates a new superpopulation-based approach put forth by Chaudhuri, Handcock and Rendall (2013), based upon the empirical likelihood of Owen (1989). Using the form of the Hajek estimator and informing it with conditional estimation on empirical likelihood, the approach is shown by simulation study to improve in both accuracy and variance against Hajek's estimator in cases where the values of interest and sampled auxiliary information have little or no correlation, and no improvement over existing methods otherwise