Survey Methodology
Variance of the generalized regression estimator under measurement error

by Jan van den Brakel and John Michiels^{Note 1}

Abstract

With the exception of two-phase sampling, the standard variance approximation of the generalized regression (GREG) estimator assumes that the population totals in the weighting scheme are observed without error. If the weighting model of the GREG estimator contains population totals that are observed with measurement error sources other than the sampling error of first-phase estimates, then this uncertainty will be ignored by the variance approximation of the GREG estimator. This paper proposes a variance approximation for the GREG estimator that accounts for additional uncertainty arising from measurement error in one or more of the population totals used in the weighting scheme. This approach has been developed for, and is being applied to, the Dutch Labour Force Survey (DLFS). The monthly publications of the DLFS are obtained with a time series model, which corrects for rotation group bias and discontinuities caused by major redesigns and the loss of face-to-face interviews during COVID-19. The GREG estimates for the quarterly figures are benchmarked to the average of the monthly publications to enforce numerical consistency between monthly and quarterly publication tables. The standard variance approximation of the GREG estimator assumes that these population totals are observed without error. This results in an underestimation of the variance of the GREG estimator. The variance approximation proposed in this paper results in more realistic standard errors for the quarterly GREG estimates.

Key Words: Calibration; Labour Force Survey; Numerical consistency between estimated tables; Variance estimation.

Table of contents

• Section 1. Introduction
• Section 2. Generalized regression estimator
• Section 3. Dutch Labour Force Survey
• Section 4. Variance of the GREG estimator under measurement error
• Section 5. Results
• Section 6. Conclusion
• Acknowledgements
• Appendix
• References

How to cite

van den Brakel, J. and Michiels, J. (2026). Variance of the generalized regression estimator under measurement error. Survey Methodology, 52(1), 95-116. Available at: http://www.statcan.gc.ca/pub/12-001-x/2026001/article/00010-eng.pdf.

Note

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