Blockwise empirical Euclidean likelihood for weakly dependent processes

Abstract

This paper introduces a method of blockwise empirical Euclidean likelihood for weakly dependent processes. The strong consistency and asymptotic normality of the blockwise empirical Euclidean likelihood estimation are proved. It is deduced that the blockwise empirical Euclidean likelihood ratio statistic is asymptotically a chi-square statistic. These results show that the blockwise empirical Euclidean likelihood estimation is more asymptotically efficient than the original empirical (Euclidean) likelihood estimation and it is useful for weakly dependent processes.