Efficient Empirical Bayes Estimates For Risk Parameters Of Pareto Distributions

Because Pareto distribution can effectively depict some characteristics of the loss data,so it has been widely used in data analysis and statistical modeling in many fields such as insurance actuarial,economics,and financial.For the parameter es-timation problems with known distribution types,the hierarchical model has been widely studied and used,and gradually becomes a very important method.Using the hierarchical model to estimate the parameters in the distribution can effectively reduce the estimation bias,therefore,in this thesis,we consider the simultaneous estimation of the risk parameters of Pareto distributions from the perspective of empirical Bayesian.Firstly,inspired by the thought of Stein's unbiased estimate of risk,this thesis constructs an unbiased estimates function for proper approximation of the risk function which are then minimized to produce effective SURE estimators.Secondly,under mild conditions,we prove the optimality of the new estimators.Fi-nally,the performance of the new method is illustrated through simulation studies,and an analysis of auto insurance claim data is also provided to show its practical usefulness.