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Regression analysis for exponential family data in a finite population setup using two-stage cluster sample

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  • Brajendra C. Sutradhar

    (Memorial University)

Abstract

Over the last four decades, the cluster regression analysis in a finite population (FP) setup for an exponential family such as linear or binary data was done by using a two-stage cluster sample chosen from the FP but by treating the sample as though it is a single-stage cluster sample from a super-population (SP) which contains the FP as a hypothetical sample. Because the responses within a cluster in the FP are correlated, the aforementioned sample mis-specification makes the sample-based so-called GLS (generalized least square) estimators design biased and inconsistent. In this paper, we demonstrate for the exponential family data how to avoid the sampling mis-specification and accommodate the cluster correlations to obtain unbiased and consistent estimates for the FP parameters. The asymptotic normality of the regression estimators is also given for the construction of confidence intervals when needed.

Suggested Citation

  • Brajendra C. Sutradhar, 2023. "Regression analysis for exponential family data in a finite population setup using two-stage cluster sample," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 75(3), pages 425-462, June.
    • Handle: RePEc:spr:aistmt:v:75:y:2023:i:3:d:10.1007_s10463-022-00850-6
    DOI: 10.1007/s10463-022-00850-6
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    References listed on IDEAS

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    1. Sutradhar, Brajendra C. & Rao, R. Prabhakar, 2001. "On Marginal Quasi-Likelihood Inference in Generalized Linear Mixed Models," Journal of Multivariate Analysis, Elsevier, vol. 76(1), pages 1-34, January.
    2. Thomas R. Ten Have & Alfredo Morabia, 1999. "Mixed Effects Models with Bivariate and Univariate Association Parameters for Longitudinal Bivariate Binary Response Data," Biometrics, The International Biometric Society, vol. 55(1), pages 85-93, March.
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