Nonidentifiability of Mixed-Model Parameters under Informative Sampling using only Single-Inclusion Weights

• Activity Number: 527 - New Approaches to Model-Assisted Survey Estimation with Informative Weights
• Type: Invited
• Date/Time: Thursday, August 6, 2020 : 1:00 PM to 2:50 PM
• Sponsor: Survey Research Methods Section
• Author(s): Eric V Slud*
• Companies: US Census Bureau
• Keywords: Biased Sampling; Consistency; Informative Sampling; Random weights; Superpopulation; Two-level model

Abstract

This paper studies the problem of consistent estimation of two-level superpopulation parameters from informatively cluster-sampled survey data, using possibly random weights. Conditions that random weights should satisfy are first formulated. Next an inclusive definition is given for informative sampling allowing for random weights. The notion of identifiability of superpopulation parameters is defined under the standard survey data structure in which (possibly random) single-inclusion weights are observed together with attribute data for sampled units. A review is given of previously proposed methods of estimation using the survey design only through the observed single-inclusion weights. Finally, a new class of informative within-cluster sampling designs is introduced and used to demonstrate exact nonidentifiability of parameters for the infinite-population-cluster biased sampling case, and asymptotic nonidentifiability for finite (large) population clusters.