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Modelling complex survey data with population level information: an empirical likelihood approach.

M Oguz-Alper1, Y G Berger2

  • 1Statistics Norway, Postboks 8131 Dep, NO-0033 Oslo, Norway , melike.oguz.alper@ssb.no.

Biometrika
|June 10, 2016
PubMed
Summary

This study demonstrates that empirical likelihood ratio statistics follow a chi-squared distribution for stratified unequal probability sampling. This method offers improved confidence intervals compared to traditional variance estimation, linearization, or resampling techniques.

Keywords:
Design-based inferenceEmpirical likelihoodEstimating equationInclusion probabilityRegression parameterUnequal probability sampling

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Area of Science:

  • Statistics
  • Survey Methodology

Background:

  • Survey data frequently involve unequal probability sampling from stratified populations.
  • Statistical modeling often includes parameters of interest alongside nuisance parameters.

Purpose of the Study:

  • To investigate the asymptotic distribution of empirical likelihood ratio statistics under stratified unequal probability sampling.
  • To compare the performance of empirical likelihood confidence intervals with standard methods.

Main Methods:

  • Utilizing empirical likelihood ratio statistics.
  • Applying to stratified single and multi-stage unequal probability sampling scenarios.
  • Conducting simulation studies to evaluate performance.

Main Results:

  • The empirical likelihood ratio statistic asymptotically follows a chi-squared distribution under the specified sampling conditions.
  • Empirical likelihood confidence intervals demonstrated superior coverage and more balanced tail error rates in simulations.

Conclusions:

  • Empirical likelihood provides a robust framework for statistical inference in complex survey designs.
  • This approach offers advantages over traditional methods for confidence interval construction in unequal probability sampling.