调整经验欧氏似然及其性质

Adjusted Empirical Euclidean Likelihood and its Properties

经验(欧氏)似然是近年来非常流行的非参数统计方法之一,但其存在凸包限制和计算复杂等不足之处.针对此不足,CHEN等人(2008)给出调整经验似然.本文借助此想法,给出调整经验欧氏似然方法,进而讨论其相应的统计性质.理论结果显示,调整经验欧氏似然有与经验欧氏似然完全类似的性质;模拟结果显示,在某些情况下(如二维情况),调整经验(欧氏)似然所得的区间估计具有较好的覆盖率.此外,调整经验欧氏似然的思想和计算都比较简单.从实用角度看,具有较高的推广价值.

Empirical（Euclidean） likelihood is one of the most popular nonparametric statistical methods in recent years. But it also involves convex hull restrictions and complex calculation problems. To solve these difficulties, CHEN et al.（2008） proposed an adjusted empirical likelihood method. Inspired by this thought, we give the adjusted empirical Euclidean likelihood method and discuss its statistical properties. It is found that the adjusted empirical Euclidean likelihood has similar properties to empirical（Euclidean） likelihood. The simulations show that in some cases（for example, the two dimension situation）, the confidence regions with adjusted empirical Euclidean likelihood method has better coverage probability. More importantly, the thoughts and calculation of adjusted empirical Euclidean likelihood are quite simple to conduct. From the practical point, it has higher application value.