Survey Methodology
Optimal linear estimation in two-phase sampling

by Takis MerkourisNote 1

  • Release date: December 15, 2022

Abstract

Two-phase sampling is a cost effective sampling design employed extensively in surveys. In this paper a method of most efficient linear estimation of totals in two-phase sampling is proposed, which exploits optimally auxiliary survey information. First, a best linear unbiased estimator (BLUE) of any total is formally derived in analytic form, and shown to be also a calibration estimator. Then, a proper reformulation of such a BLUE and estimation of its unknown coefficients leads to the construction of an “optimal” regression estimator, which can also be obtained through a suitable calibration procedure. A distinctive feature of such calibration is the alignment of estimates from the two phases in an one-step procedure involving the combined first-and-second phase samples. Optimal estimation is feasible for certain two-phase designs that are used often in large scale surveys. For general two-phase designs, an alternative calibration procedure gives a generalized regression estimator as an approximate optimal estimator. The proposed general approach to optimal estimation leads to the most effective use of the available auxiliary information in any two-phase survey. The advantages of this approach over existing methods of estimation in two-phase sampling are shown both theoretically and through a simulation study.

Key Words: Auxiliary information; Best linear unbiased estimation; Calibration; Generalized regression estimation; Double sampling.

Table of contents

How to cite

Merkouris, T. (2022). Optimal linear estimation in two-phase sampling. Survey Methodology, Statistics Canada, Catalogue No. 12-001-X, Vol. 48, No. 2. Paper available at http://www.statcan.gc.ca/pub/12-001-x/2022002/article/00011-eng.htm.

Note


Report a problem on this page

Is something not working? Is there information outdated? Can't find what you're looking for?

Please contact us and let us know how we can help you.

Privacy notice

Date modified: