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A unified approach to regression analysis under double‐sampling designs

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  • Yi‐Hau Chen
  • Hung Chen

Abstract

We propose a unified approach to the estimation of regression parameters under double‐sampling designs, in which a primary sample consisting of data on the rough or proxy measures for the response and/or explanatory variables as well as a validation subsample consisting of data on the exact measurements are available. We assume that the validation sample is a simple random subsample from the primary sample. Our proposal utilizes a specific parametric model to extract the partial information contained in the primary sample. The resulting estimator is consistent even if such a model is misspecified, and it achieves higher asymptotic efficiency than the estimator based only on the validation data. Specific cases are discussed to illustrate the application of the estimator proposed.

Suggested Citation

  • Yi‐Hau Chen & Hung Chen, 2000. "A unified approach to regression analysis under double‐sampling designs," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 62(3), pages 449-460.
    • Handle: RePEc:bla:jorssb:v:62:y:2000:i:3:p:449-460
    DOI: 10.1111/1467-9868.00243
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    Cited by:

    1. Yang Zhao, 2022. "Diagnostic checking of multiple imputation models," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 106(2), pages 271-286, June.
    2. Song Xi Chen & Denis H. Y. Leung & Jing Qin, 2008. "Improving semiparametric estimation by using surrogate data," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 70(4), pages 803-823, September.
    3. Mengling Liu & Wenbin Lu & Chi-hong Tseng, 2010. "Cox Regression in Nested Case–Control Studies with Auxiliary Covariates," Biometrics, The International Biometric Society, vol. 66(2), pages 374-381, June.
    4. Zheng, Ming & Yu, Wen, 2011. "An empirical likelihood approach to data analysis under two-stage sampling designs," Statistics & Probability Letters, Elsevier, vol. 81(8), pages 947-956, August.
    5. Denis Heng Yan Leung & Ken Yamada & Biao Zhang, 2015. "Enriching Surveys with Supplementary Data and its Application to Studying Wage Regression," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 42(1), pages 155-179, March.
    6. Jason P. Estes & Bhramar Mukherjee & Jeremy M. G. Taylor, 2018. "Empirical Bayes Estimation and Prediction Using Summary-Level Information From External Big Data Sources Adjusting for Violations of Transportability," Statistics in Biosciences, Springer;International Chinese Statistical Association, vol. 10(3), pages 568-586, December.
    7. Chi-Chung Wen & Yi-Hau Chen, 2014. "Semiparametric analysis of incomplete current status outcome data under transformation models," Biometrics, The International Biometric Society, vol. 70(2), pages 335-345, June.
    8. Yang Zhao & Meng Liu, 2021. "Unified approach for regression models with nonmonotone missing at random data," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 105(1), pages 87-101, March.

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