Transforming the empirical likelihood towards better accuracy

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 (c) 2017 Statistical Society of Canada