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An empirical likelihood approach under cluster sampling with missing observations

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  • Yves G. Berger

    (University of Southampton)

Abstract

The parameter of interest considered is the unique solution to a set of estimating equations, such as regression parameters of generalised linear models. We consider a design-based approach; that is, the sampling distribution is specified by stratification, cluster (multi-stage) sampling, unequal selection probabilities, side information and a response mechanism. The proposed empirical likelihood approach takes into account of these features. Empirical likelihood has been mostly developed under more restrictive settings, such as independent and identically distributed assumption, which is violated under a design-based framework. A proper empirical likelihood approach which deals with cluster sampling, missing data and multidimensional parameters is absent in the literature. This paper shows that a cluster-level empirical log-likelihood ratio statistic is pivotal. The main contribution of the paper is to provide the rigorous asymptotic theory and underlining regularity conditions which imply $${\surd {n}}$$√n-consistency and the Wilks’s theorem or self-normalisation property. Negligible and large sampling fractions are considered.

Suggested Citation

  • Yves G. Berger, 2020. "An empirical likelihood approach under cluster sampling with missing observations," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 72(1), pages 91-121, February.
    • Handle: RePEc:spr:aistmt:v:72:y:2020:i:1:d:10.1007_s10463-018-0681-x
    DOI: 10.1007/s10463-018-0681-x
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    References listed on IDEAS

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    8. Qihua Wang, 2002. "Empirical likelihood-based inference in linear errors-in-covariables models with validation data," Biometrika, Biometrika Trust, vol. 89(2), pages 345-358, June.
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    Cited by:

    1. Berger, Yves G. & Patilea, Valentin, 2022. "A semi-parametric empirical likelihood approach for conditional estimating equations under endogenous selection," Econometrics and Statistics, Elsevier, vol. 24(C), pages 151-163.
    2. Rami V. Tabri & Mathew J. Elias, 2024. "Testing for Restricted Stochastic Dominance under Survey Nonresponse with Panel Data: Theory and an Evaluation of Poverty in Australia," Papers 2406.15702, arXiv.org.

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