Survey Methodology
Generalized regression estimation under misspecified sample design

by Joseph D. Engmark and Jean D. OpsomerNote 1

  • Release date: Dedcember 23, 2025
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Abstract

Classical design-based survey estimation relies on a properly specified sampling design for valid inference. We consider the properties of regression estimation under a misspecified sample design, in which the nominal and true inclusion probabilities do not necessarily match. This general misspecified sample design setting encompasses many challenges in the modern survey environment. Under this setting, an asymptotic analysis of the regression estimator, an expression of the bias, and an expression of the variance are presented. Further, a consistent variance estimator is derived and an expression which estimates the bias in-part or in-whole is discussed. This later expression may be used as an indicator of the presence of bias due to misspecification by a practitioner. A simulation study is conducted to support the presented theory.

Key Words:    Design-based; Model-assisted; Probability sampling; Survey asymptotics; Survey sampling.

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How to cite

Engmark, J.D. and Opsomer, J.D. (2025). Generalized regression estimation under misspecified sample design. Survey Methodology, 51(2), 475-491. Paper available at http://www.statcan.gc.ca/pub/12-001-x/2025002/article/00008-eng.pdf.

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ISSN : 1492-0921

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Survey Methodology publishes articles dealing with various aspects of statistical development relevant to a statistical agency, such as design issues in the context of practical constraints, use of different data sources and collection techniques, total survey error, survey evaluation, research in Survey Methodology, time series analysis, seasonal adjustment, demographic studies, data integration, estimation and data analysis methods, and general survey systems development. The emphasis is placed on the development and evaluation of specific methodologies as applied to data collection or the data themselves. All papers will be refereed. However, the authors retain full responsibility for the contents of their papers and opinions expressed are not necessarily those of the Editorial Board or of Statistics Canada.

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Published by authority of the Minister responsible for Statistics Canada.

© His Majesty the King in Right of Canada, as represented by the Minister of Industry, 2025

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Catalogue No. 12-001-X

Frequency: Semi-annual

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