Ratio Estimation of the Mean with Unequal Probability Samples: Hansen, Madow, and Tepping Revisited

• Activity Number: 99
• Type: Topic Contributed
• Date/Time: Monday, August 3, 2009 : 8:30 AM to 10:20 AM
• Sponsor: Section on Survey Research Methods
• Author(s): Fotios Kokkotos*+ and Roderick J.A. Little
• Companies: Trinity Partners LLC and University of Michigan
• Keywords: Bayesian Methods ; Design-based inference ; Robustness ; Sampling Weights ; Survey Sampling ; Simulation

Abstract

In a famous paper on the design-based approach to survey inference, Hansen, Madow, and Tepping (1983) (HMT) consider estimation of the finite population mean of a variable Y from unequal probability samples, with an auxiliary variable X measured for all units in the population. They compare the ratio model estimator and the design-weighted combined ratio estimator and show in simulations that the "model-based estimator" can be seriously biased for the population mean even under moderate violations of the ratio model, whereas the "design-based estimator" has better frequency properties. From a robust Bayesian perspective, both of these estimators have limitations discussed in Little's paper (2004). The robust Bayesian approach leads to the separate ratio estimator and its shrinkage-type modifications for small samples. These alternatives are compared with the HMT estimators by simulation.