Doubly Robust Estimation of the Finite Population Distribution Function Using Nonprobability Samples

Soonpil Kwon, Dongmin Jang and Kyu-Seong Kim ()
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Soonpil Kwon: Department of Statistics and Data Science, University of Seoul, 163 Seoulsiripdae-ro, Dongdaemun-gu, Seoul 02504, Republic of Korea
Dongmin Jang: Department of Statistics and Data Science, University of Seoul, 163 Seoulsiripdae-ro, Dongdaemun-gu, Seoul 02504, Republic of Korea
Kyu-Seong Kim: Department of Statistics, University of Seoul, 163 Seoulsiripdae-ro, Dongdaemun-gu, Seoul 02504, Republic of Korea

Mathematics, 2025, vol. 13, issue 19, 1-16

Abstract: The growing use of nonprobability samples in survey statistics has motivated research on methodological adjustments that address the selection bias inherent in such samples. Most studies, however, have concentrated on the estimation of the population mean. In this paper, we extend our focus to the finite population distribution function and quantiles, which are fundamental to distributional analysis and inequality measurement. Within a data integration framework that combines probability and nonprobability samples, we propose two estimators, a regression estimator and a doubly robust estimator, and discuss their asymptotic properties. Furthermore, we derive quantile estimators and construct Woodruff confidence intervals using a bootstrap method. Simulation results based on both a synthetic population and the 2023 Korean Survey of Household Finances and Living Conditions demonstrate that the proposed estimators perform stably across scenarios, supporting their applicability to the production of policy-relevant indicators.

Keywords: data integration; inverse probability weighting; quantiles; regression (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2025
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