We extend the empirical likelihood beyond its domain by expanding its contours nested inside the domain with a similarity transformation. The extended empirical likelihood achieves two objectives at the same time: escaping the “convex hull constraint” on the empirical likelihood and improving the coverage accuracy of the empirical likelihood ratio confidence region to O(n^-2). The latter is accomplished through a special transformation which matches the extended empirical likelihood with the Bartlett corrected empirical likelihood. The extended empirical likelihood ratio confidence region retains the shape of the original empirical likelihood ratio confidence region. It also accommodates adjustments for dimension and small sample size, giving it good coverage accuracy in large and small sample situations. The Canadian Journal of Statistics 41: 257–274; 2013© 2013 Statistical Society of Canada
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