On variance estimation under complex sampling designs

Abstract

This thesis is formed of three manuscripts (chapters) about variance estimation. Each of the chapters focuses on developing new original variance estimators. The Chapter 1 proposes a novel jackknife variance estimator for self weighted two-stage sampling. Customary jackknifes for these designs rely only on the first sampling stage. This omission may induce a bias in the variance estimation when cluster sizes vary, second stage sampling fractions are small or when there is low variability between clusters. The proposed jackknife accounts of all sampling stages via deletion of clusters and observations within clusters. It does not need join-inclusion probabilities and naturally includes finite population corrections. Its asymptotic design-consistency is shown. A simulation study show that it can be more accurate than the customary jackknife used for this kind of sampling designs (Rao, Wu and Yue, 1992). The Chapter 2 proposes a totally new replication variance estimator for any unequal-probability without-replacement sampling design. The proposed replication estimator is approximately equal to the linearisation variance estimators obtained by the Demnati and Rao (2004) approach. It is more general than the Campbell (1980); Berger and Skinner (2005) generalised jackknife. Its asymptotic design consistency is shown. A simulation study shows it is more stable than standard jackknifes (Quenouille, 1956; Tukey, 1958) with ad hoc finite population corrections and than the generalised jackknife (Campbell, 1980; Berger and Skinner, 2005). The Chapter 3 proposes a new variance estimator which accounts the item non-response under unequal-probability without-replacement sampling when estimating a change from rotating (overlapping) repeated surveys. The proposed estimator combines the original approach by Berger and Priam (2010, 2012) and the non response reverse approach for variance estimation (Fay, 1991; Shao and Steel, 1999). It gives design-consistent estimation of the variance of change when the sampling fraction is small. The proposed estimator uses random Hot-deck imputation, but it can be implemented with other imputation techniques. Further, there are two more complementary chapters. One introduces the R package called samplingVarEst which implements of some methods for variance estimation utilised for the simulations. Finally, there is a brief chapter which discusses future research work.

More information

Identifiers

ORCID for Yves G. Berger: orcid.org/0000-0002-9128-5384

Catalogue record

Export record