For a single stage fixed size unequal probability sampling design we describe a method of bootstrap resampling and investigate its performance in estimation of variance of a Horvitz-Thompson estimator, and estimation of the mean squared error of the solution of an unbiased estimating equation. Extensions to the context of a system of estimating functions are considered. We then quantify the effectiveness of the resampling method in correcting the bias of estimators of a population variance, and estimating the mean squared error and other aspects of the distribution of population variance estimators. The technique is applied to inference for variance components of a two-level model with continuous outcomes when the sampling design, which may be informative, is carried out in stages corresponding to the levels. Simulation studies show it to work well for inference even when the sample size at the lowest level is small.
Keywords: Variance components; Complex surveys; Multilevel models; Resampling
Biography: Dr. Thompson is University Professor Emeritus of Statistics at the University of Waterloo. Her interests in survey methodology are currently focussed on analysis of survey data with complex structure. She is the author of a monograph entitled “Theory of Sample Surveys”.