Modelling complex survey data with population level information: an empirical likelihood approach.
Survey data are often collected with unequal probabilities from a stratified population. In many modelling situations, the parameter of interest is a subset of a set of parameters, with the others treated as nuisance parameters. We show that in this situation the empirical likelihood ratio statistic follows a chi-squared distribution asymptotically, under stratified single and multi-stage unequal probability sampling, with negligible sampling fractions. Simulation studies show that the empirical likelihood confidence interval may achieve better coverages and has more balanced tail error rates than standard approaches involving variance estimation, linearization or resampling.
Statistics Norway, Postboks 8131 Dep, NO-0033 Oslo, Norway , melike.oguz.alper@ssb.no.
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M
Oguz-Alper
Southampton Statistical Sciences Research Institute, University of Southampton, Southampton SO17 1BJ, U.K. , y.g.berger@soton.ac.uk.
Y G
YG
Berger
Design-based inference; Empirical likelihood; Estimating equation; Inclusion probability; Regression parameter; Unequal probability sampling