The variance of the Horvitz-Thompson estimator under a complex unequal probability without-replacement (WOR) sampling design is often approximated by its variance under the multinomial design. In this presentation we consider the respective variance ratio. The ratio does not exceed one for the Sampford and the Conditional Poisson sampling designs, irrespective of the population values (Gabler 1981, Qualite 2008). In the presentation, we will put forward some more WOR designs with this property. Moreover, for some designs we are able to sharpen the bound with an exact expression of the first and second order inclusion probabilities. We use distributional approach on sampling designs (Traat et al. 2004).

References:

Gabler, S. (1981) A comparison of Sampford's sampling procedure versus unequal probability sampling with replacement. Biometrica 68, 725-727.

Traat, I., Bondesson, L., Meister, K. (2004) Sampling design and sample selection through distribution theory. J. Statist. Plann. Inference 123, 395-413.

Qualite, L. (2008) A comparison of conditional Poisson sampling versus unequal probability sampling with replacement. J. Statist. Plann. Inference 138, 1428-1432.

Keywords: Horvitz-Thompson estimator; Bound of the variance ratio; WOR-design

Biography: Dr. Imbi Traat is Associate Professor at University of Tartu. Her primary study area is survey sampling theory and methodology. She is Estonian coordinator of the Baltic-Nordic-Ukrainian network in this field. She is president of the Estonian Statistical Society.