Generalized Multiplicity-Adjusted Multiple Frame Estimation via Regression

A class of generalized multiplicity-adjusted Horvitz-Thompson (GMHT) estimators was proposed by Singh and Mecatti (2011) to provide a unified and systematic approach to existing estimators motivated from considerations of available frame level information leading to separate and combined frame approaches. Under availability of information about selected units from the sampled frame only, separate frame estimators can be obtained by regression of the basic MHT estimator on predictors (or zero functions) formed from multiple estimators for overlapping domains. However, if full information regarding selection probabilities from all possible frames a unit could have been selected is available, estimators under the combined approach can be obtained by regression of the full MHT estimator on predictors from overlapping domains. The unified framework uses zero functions in regression which play a fundamental role in statistical estimation such as quasi-likelihood estimation. It allows us to propose new and improved estimators over other estimators such as optimal regression and pseudo maximum likelihood estimators while preserving their essential features. The class of GMHT-regression estimators is constructed as sums of contributions from each frame which allow for application of standard variance estimation techniques. Results based on a limited simulation study are presented to compare various estimators.