Unconditional variance estimation under complex surveys: unconditional variance estimation
Unconditional variance estimation under complex surveys: unconditional variance estimation
The unconditional framework treats the samples and the variables of interest as random variables. This is particularly suitable with analytic inference, when modelling survey data. We show that variance estimation does not involve finite population corrections and joint‐inclusion probabilities, even with large sampling fractions and under sampling without‐replacement. The main advantage of the variance estimator is its simplicity. We show that it is asymptotically unbiased, under unequal probability designs incorporating stratification, multistage and informative sampling. We consider a general class of parameters defined by estimating equations, such as means, ratios, quantiles and parameters of generalised linear models. We also show how auxiliary information can be incorporated. A test statistic is derived for hypotheses on parameters. We propose a consistent variance estimator under ordered systematic sampling.
design-based inference, estimating equation, generalised linear models, inclusion probabilities, informative sampling, model-based inference, multi-stage sampling, testing, systematic sampling, multistage sampling
Berger, Yves
8fd6af5c-31e6-4130-8b53-90910bf2f43b
Berger, Yves
8fd6af5c-31e6-4130-8b53-90910bf2f43b
Berger, Yves
(2025)
Unconditional variance estimation under complex surveys: unconditional variance estimation.
International Statistical Review.
(doi:10.1111/insr.70001).
(In Press)
Abstract
The unconditional framework treats the samples and the variables of interest as random variables. This is particularly suitable with analytic inference, when modelling survey data. We show that variance estimation does not involve finite population corrections and joint‐inclusion probabilities, even with large sampling fractions and under sampling without‐replacement. The main advantage of the variance estimator is its simplicity. We show that it is asymptotically unbiased, under unequal probability designs incorporating stratification, multistage and informative sampling. We consider a general class of parameters defined by estimating equations, such as means, ratios, quantiles and parameters of generalised linear models. We also show how auxiliary information can be incorporated. A test statistic is derived for hypotheses on parameters. We propose a consistent variance estimator under ordered systematic sampling.
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Accepted/In Press date: 1 July 2025
Keywords:
design-based inference, estimating equation, generalised linear models, inclusion probabilities, informative sampling, model-based inference, multi-stage sampling, testing, systematic sampling, multistage sampling
Identifiers
Local EPrints ID: 504096
URI: http://eprints.soton.ac.uk/id/eprint/504096
ISSN: 0306-7734
PURE UUID: 7fa62f50-238a-4b91-b4f2-89ebab9519a4
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Date deposited: 26 Aug 2025 16:36
Last modified: 18 Oct 2025 01:37
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