Survey Methodology
Estimation and inference of domain means subject to qualitative constraints

by Cristian Oliva-Aviles, Mary C. Meyer and Jean D. OpsomerNote 1

  • Release date: December 15, 2020
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Abstract

In many large-scale surveys, estimates are produced for numerous small domains defined by cross-classifications of demographic, geographic and other variables. Even though the overall sample size of such surveys might be very large, samples sizes for domains are sometimes too small for reliable estimation. We propose an improved estimation approach that is applicable when “natural” or qualitative relationships (such as orderings or other inequality constraints) can be formulated for the domain means at the population level. We stay within a design-based inferential framework but impose constraints representing these relationships on the sample-based estimates. The resulting constrained domain estimator is shown to be design consistent and asymptotically normally distributed as long as the constraints are asymptotically satisfied at the population level. The estimator and its associated variance estimator are readily implemented in practice. The applicability of the method is illustrated on data from the 2015 U.S. National Survey of College Graduates.

Key Words:      Design-based estimation; Monotone estimation; National Survey of College Graduates.

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How to cite

Oliva-Aviles, C., Meyer, M.C. and Opsomer, J.D. (2020). Estimation and inference of domain means subject to qualitative constraints. Survey Methodology, Statistics Canada, Catalogue No. 12-001-X, Vol. 46, No. 2. Paper available at https://www150.statcan.gc.ca/n1/pub/12-001-x/2020002/article/00002-eng.htm.

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ISSN : 1492-0921

Editorial policy

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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Survey Methodology is published twice a year in electronic format. Authors are invited to submit their articles in English or French in electronic form, preferably in Word to the Editor, (statcan.smj-rte.statcan@canada.ca, Statistics Canada, 150 Tunney’s Pasture Driveway, Ottawa, Ontario, Canada, K1A 0T6). For formatting instructions, please see the guidelines provided in the journal and on the web site (www.statcan.gc.ca/SurveyMethodology).

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Published by authority of the Minister responsible for Statistics Canada.

© Her Majesty the Queen in Right of Canada as represented by the Minister of Industry, 2020

Use of this publication is governed by the Statistics Canada Open Licence Agreement.

Catalogue No. 12-001-X

Frequency: Semi-annual

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Table of contents

Abstract - Article main page
Section 1. Introduction
Section 2. Constrained estimation and inference for domain means
Section 3. Properties of the constrained estimator
Section 4. Performance of constrained estimator
Section 5. Application of constrained estimator to NSCG
Section 6. Conclusions
Appendix
References

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