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Empirical likelihood‐based inferences for a low income proportion
Author(s) -
Yang Baoying,
Qin Gengsheng,
Qin Jing
Publication year - 2011
Publication title -
canadian journal of statistics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.804
H-Index - 51
eISSN - 1708-945X
pISSN - 0319-5724
DOI - 10.1002/cjs.10087
Subject(s) - econometrics , index (typography) , statistics , economics , estimation , confidence interval , poverty , welfare economics , mathematics , geography , economic growth , management , world wide web , computer science
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