Empirical likelihood confidence intervals for complex sampling designs


Berger, Y.G. and De La Riva Torres, O. (2012) Empirical likelihood confidence intervals for complex sampling designs. Southampton, GB, Southampton Statistical Sciences Research Institute, 22pp. (S3RI Methodology Working Papers).

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Description/Abstract

We propose an empirical likelihood approach which gives design-based confidence intervals which can be calculated without the need of variance estimates, design-effects, resampling, joint-inclusion probabilities and linearisation, even when the estimator of interest is not linear. It can be used to construct confidence intervals for a large class of sampling designs and estimators which are solutions of estimating equations. It can be used for means, regressions coefficients, quantiles, totals or counts even when the population size is unknown. It can be used with large sampling fractions. It also provides asymptotically design optimal point estimators, and naturally includes calibration constraints. Our proposed approach can be viewed as an extension of the empirical likelihood approach to complex survey data. The proposed approach is computationally simpler than the pseudo empirical likelihood and the bootstrap approaches. The simulation study shows that the proposed confidence interval may give better coverages than the confidence intervals based on linearisation, bootstrap and pseudo empirical likelihood. Our simulation study shows that under complex sampling designs, standard confidence intervals based upon normality may have poor coverages, because the point estimator may not follow a normal sampling distribution and its variance estimator may be biased.

Item Type: Monograph (Working Paper)
Keywords: calibration, design-based approach, finite population corrections, h´ajek estimator, horvitz-thompson estimator, regression estimator, stratification, unequal inclusion probabilities
Subjects: H Social Sciences > HA Statistics
Divisions: University Structure - Pre August 2011 > Southampton Statistical Sciences Research Institute
Faculty of Social and Human Sciences > Social Sciences > Social Statistics & Demography
ePrint ID: 337688
Date Deposited: 01 May 2012 15:25
Last Modified: 07 May 2014 11:34
URI: http://eprints.soton.ac.uk/id/eprint/337688

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