Adjusted Empirical Likelihood of Multivariate Density Functions
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.
multidimensional density functionadjusted empirical likelihoodconfidence interval
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