High Order Adjusted Block-wise Empirical Likelihood For Weakly Dependent Data

It is well known that the empirical likelihood ratio confidence region suffers finite sample under-coverage issue, and this severely hampers its application in statistical inferences.} The root cause of this under-coverage is an upper limit imposed by the convex hull of the estimating functions that is used in the construction of the profile empirical likelihood. For i.i.d data, various methods have been proposed to solve this issue by modifying the convex hull, but it is not clear how well these methods perform when the data are no longer independent. In this paper, we propose an adjusted blockwise empirical likelihood that is designed for weakly dependent multivariate data. We show that our method not only preserves the much celebrated asymptotic $\chi^2-$distribution, but also improves the finite sample coverage probability by removing the upper limit imposed by the convex hull. Further, we show that our method is also Bartlett correctable, thus is able to achieve high order asymptotic coverage accuracy.