Empirical Likelihood Statistical Inference for Compound Poisson Vector Processes under Infinite Covariance Matrix.

The paper discusses the statistical inference problem of the compound Poisson vector process (CPVP) in the domain of attraction of normal law but with infinite covariance matrix. The empirical likelihood (EL) method to construct confidence regions for the mean vector has been proposed. It is a generalization from the finite second-order moments to the infinite second-order moments in the domain of attraction of normal law. The log-empirical likelihood ratio statistic for the average number of the CPVP converges to F distribution in distribution when the population is in the domain of attraction of normal law but has infinite covariance matrix. Some simulation results are proposed to illustrate the method of the paper. [ABSTRACT FROM AUTHOR]