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Transforming the empirical likelihood towards better accuracy
Author(s) -
Jing BingYi,
Tsao Min,
Zhou Wang
Publication year - 2017
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.11328
Subject(s) - empirical likelihood , consistency (knowledge bases) , inference , computer science , computation , econometrics , empirical research , likelihood principle , likelihood function , simple (philosophy) , statistical inference , statistics , mathematics , maximum likelihood , algorithm , quasi maximum likelihood , artificial intelligence , philosophy , epistemology
Under‐coverage has been a long‐standing issue with the empirical likelihood confidence region. Several methods can be used to address this issue, but they all add complexity to the empirical likelihood inference requiring extra computation and/or extra theoretical investigation. The objective of this article is to find a method that does not add complexity. To this end we look for a simple transformation of the empirical likelihood to alleviate the under‐coverage. Using several criteria concerning the accuracy, consistency, and preservation of the geometric appeal of the original empirical likelihood we obtain a transformed version of the empirical likelihood that is extremely simple in theory and computation. Its confidence regions are surprisingly accurate, even in small sample and multidimensional situations. It can be easily used to alleviate the under‐coverage problem of empirical likelihood confidence regions. The Canadian Journal of Statistics 45: 340–352; 2017 © 2017 Statistical Society of Canada