Empirical likelihood‐based inferences for a low income proportion |
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| Authors: | Baoying Yang Gengsheng Qin Jing Qin |
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| Institution: | 1. College of Mathematics, Sichuan University, Chengdu, Sichuan 610064, China;2. Department of Mathematics and Statistics, Georgia State University, Atlanta, GA 30302, USA;3. National Institute of Allergy and Infectious Diseases, NIH, Bethesda, MD 20892, USA |
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| Abstract: | Low income proportion is an important index in comparisons of poverty in countries around the world. The stability of a society depends heavily on this index. An accurate and reliable estimation of this index plays an important role for government's economic policies. In this paper, the authors study empirical likelihood‐based inferences for a low income proportion under the simple random sampling and stratified random sampling designs. It is shown that the limiting distributions of the empirical likelihood ratios for the low income proportion are the scaled chi‐square distributions. The authors propose various empirical likelihood‐based confidence intervals for the low income proportion. Extensive simulation studies are conducted to evaluate the relative performance of the normal approximation‐based interval, bootstrap‐based intervals, and the empirical likelihood‐based intervals. The proposed methods are also applied to analyzing a real economic survey income dataset. The Canadian Journal of Statistics 39: 1–16; 2011 ©2011 Statistical Society of Canada |
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| Keywords: | Bootstrap confidence interval economic policy empirical likelihood low income proportion relative poverty line survey sampling Primary 62G20 secondary 62D05 |
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