多元密度函数的调整经验似然

Adjusted Empirical Likelihood of Multivariate Density Functions

研究独立样本情形多维密度函数调整经验似然置信区间的构造,证明了独立样本多维密度函数调整经验似然比统计量的极限分布为卡方分布,且证明了备择假设下调整经验似然的渐近性质,并通过模拟对比分析了调整经验似然、经验似然、正态逼近三种构造置信区间的方法.结果表明,对于多元密度函数置信区间的构造,调整经验似然的覆盖率更接近给定的名义置信水平,因此调整经验似然的表现优于经验似然和正态逼近.

In this paper,we study the construction of the confidence interval of the adjusted empirical likelihood of the multi-dimensional density function for independent samples.We prove that the limit distribution of the adjusted empirical likelihood ratio statistic of the multi-dimensional density function for independent samples is the chi-square distribution,and prove the asymptotic property of the adjusted empirical likelihood under the alternative hypothesis.Three methods of constructing confidence intervals,namely adjusting empirical likelihood,empirical likelihood and normal approximation are analyzed by simulation.The results show that for the confidence interval construction of multivariate density function,the coverage of the adjusted empirical likelihood is closer to the given nominal confidence level,so the adjusted empirical likelihood performs better than the empirical likelihood and the normal approximation.