Open Access
September, 1981 Inference From Stratified Samples: Properties of the Linearization, Jackknife and Balanced Repeated Replication Methods
D. Krewski, J. N. K. Rao
Ann. Statist. 9(5): 1010-1019 (September, 1981). DOI: 10.1214/aos/1176345580

Abstract

The asymptotic normality of both linear and nonlinear statistics and the consistency of the variance estimators obtained using the linearization, jackknife and balanced repeated replication (BRR) methods in stratified samples are established. The results are obtained as $L \rightarrow \infty$ within the context of a sequence of finite populations $\{\Pi_L\}$ with $L$ strata in $\Pi_L$ and are valid for any stratified multistage design in which the primary sampling units (psu's) are selected with replacement and in which independent subsamples are taken within those psu's selected more than once. In addition, some exact analytical results on the bias and stability of these alternative variance estimators in the case of ratio estimation are obtained for small $L$ under a general linear regression model.

Citation

Download Citation

D. Krewski. J. N. K. Rao. "Inference From Stratified Samples: Properties of the Linearization, Jackknife and Balanced Repeated Replication Methods." Ann. Statist. 9 (5) 1010 - 1019, September, 1981. https://doi.org/10.1214/aos/1176345580

Information

Published: September, 1981
First available in Project Euclid: 12 April 2007

zbMATH: 0474.62013
MathSciNet: MR628756
Digital Object Identifier: 10.1214/aos/1176345580

Subjects:
Primary: 62D05

Keywords: balanced repeated replication , bias , central limit theorem , Jackknife method , linearization method , ratio estimation , stability , stratified sampling , variance estimation

Rights: Copyright © 1981 Institute of Mathematical Statistics

Vol.9 • No. 5 • September, 1981
Back to Top