The Large Sample Behavior Of Distributed Moment Ratio Estimator For Extreme Value Index

Conducting extreme value analysis usually requires dealing with large datasets.Such datasets may be stored in multiple machines.Based on the divide-and-conquer algorithm and the moment ratio estimator,this paper mainly constructed the distributed moment ratio estimator when datasets are stored separately.And then investigate the large sample properties of the estimator under the second-order regular variation condition.We assume that the observations X1,...,Xnare stored in k machines with m observations each.And construct the distributed moment ratio estimator using samples from each machine.Simulation studies are illustrated to compare the distributed Hill estimator and the distributed moment ratio estimator.When the observations stored in multiple machines are i.i.d,we investigate the weak convergence and asymptotic normality of the distributed moment ratio estimator under the second-order regular variation condition in section 2.We further study the case when observations on different machines follow different distributions and prove the asymptotical normality of the estimator in sections 3.In section 4,we compared the distributed moment ratio estimator with the distributed Hill estimator when X1,...,Xnare i.i.d random variables.At last,the distributed moment ratio estimator is used on car insurance claims data to estimate the heavy-tailed extreme value index,and the results shows that the estimate is acceptable.