The Annals of Statistics

Inference From Stratified Samples: Properties of the Linearization, Jackknife and Balanced Repeated Replication Methods

D. Krewski and J. N. K. Rao

Full-text: Open access

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.

Article information

Source
Ann. Statist., Volume 9, Number 5 (1981), 1010-1019.

Dates
First available in Project Euclid: 12 April 2007

Permanent link to this document
https://projecteuclid.org/euclid.aos/1176345580

Digital Object Identifier
doi:10.1214/aos/1176345580

Mathematical Reviews number (MathSciNet)
MR628756

Zentralblatt MATH identifier
0474.62013

JSTOR
links.jstor.org

Subjects
Primary: 62D05: Sampling theory, sample surveys

Keywords
Stratified sampling variance estimation linearization method jackknife method balanced repeated replication central limit theorem ratio estimation bias stability

Citation

Krewski, D.; Rao, J. N. K. Inference From Stratified Samples: Properties of the Linearization, Jackknife and Balanced Repeated Replication Methods. Ann. Statist. 9 (1981), no. 5, 1010--1019. doi:10.1214/aos/1176345580. https://projecteuclid.org/euclid.aos/1176345580


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