Comparison of Variance Estimators under Rao-Sampford Method: A Simulation Study

• Activity Number: 229
• Type: Contributed
• Date/Time: Tuesday, August 10, 2004 : 10:30 AM to 12:20 PM
• Sponsor: Section on Survey Research Methods
• Author(s): Fulvia Mecatti*+ and David Haziza and Jon N.K. Rao
• Companies: University of Milan-Bicocca and Statistics Canada and Carleton University
• Keywords: approximate joint inclusion probabilities ; efficiency ; relative bias ; unequal probability sampling without replacement

Abstract

Rao-Sampford method of unequal probability sampling without replacement has several desirable properties: inclusion probabilities are exactly proportional to sizes, Sen-Yates-Grundy exactly unbiased variance estimator is non-negative for any sample size, and variance of the estimator is always smaller than the corresponding variance under unequal probability sampling with replacement. Moreover, exact joint inclusion probabilities, and hence the exact variance estimate, can be readily calculated for any sample size, using SAS software. But several approximate variance estimators, based on approximating the joint inclusion probabilities in terms of the first order inclusion probabilities only, have been proposed in the literature. Using simulations, we first compare the relative bias (RB) of the approximate variance estimators, by varying sample size, the population size and the coefficient of variation of the auxiliary variable. We then select those that perform well in terms of RB and compare them with the exact variance estimator in terms of mean squared error.