Survey Methodology
Optimal linear estimation in two-phase sampling
- 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
- Section 1. Introduction
- Section 2. Two-phase sampling design: Structure and notation
- Section 3. Best linear unbiased estimation in two-phase sampling
- Section 4. Optimal linear estimation in two-phase sampling
- Section 5. A two-phase generalized regression estimator
- Section 6. Comparisons with existing methods
- Section 7. Simulation study
- Section 8. Discussion
- Appendix
- References
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.
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