Variance Approximation Approaches For The Local Pivotal Method

Author

Theodore Edward Owen

Year of Award

2021

Document Type

Dissertation

Degree Type

Doctor of Philosophy (PhD)

Degree Name

Mathematics

Department or School/College

Department of Mathematical Sciences

Committee Chair

David Patterson

Commitee Members

David Affleck, Jonathan Graham, Brian Steele, Johnathan Bardsley

Abstract

The problem of estimating the variance of the Horvitz-Thompson estimator of the population total when selecting a sample with unequal inclusion probabilities using the local pivotal method is discussed and explored. Samples are selected using unequal inclusion probabilities so that the estimates using the Horvitz-Thompson estimator will have smaller variance than for simple random samples. The local pivotal method is one sampling method which can select samples with unequal inclusion probability without replacement. The local pivotal method also balances on other available auxiliary information so that the variability in estimates can be reduced further.

A promising variance estimator, bootstrap subsampling, which combines bootstrapping with rescaling to produce estimates of the variance is described and developed. This new variance estimator is compared to other estimators such as naive bootstrapping, the jackknife, the local neighborhood variance estimator of Stevens and Olsen, and the nearest neighbor estimator proposed by Grafstrom.

For five example populations, we compare the performance of the variance estimators. The local neighborhood variance estimator performs best where it is appropriate. The nearest neighbor estimator performs second best and is more widely applicable. The bootstrap subsample variance estimator tends to underestimate the variance.

Recommended Citation

Owen, Theodore Edward, "Variance Approximation Approaches For The Local Pivotal Method" (2021). Graduate Student Theses, Dissertations, & Professional Papers. 11772.
https://scholarworks.umt.edu/etd/11772