Jackknife Bayesian Estimation Of Parameters Of The Poisson Distribution Under Several Loss Functions

Parameter estimation is an important part of statistical inference.How to reduce the bias of parameter estimation and improve the accuracy of estimation is the key to judge whether the estimation is effective or not.In the classical Bayesian statistical inference and statistical decision,the performance of Bayes estimation mainly depends on the form of the loss function,and different loss function has different Bayes estimation bias.For the small sample data,the Jackknife method is not limited by the type of statistical distribu-tion of parameters and can effectively reduce the estimation bias.In this paper,based on Bayesian statistical inference and statistical decision ideas and the Jackknife method,we choose the conjugate prior distribution of Poisson distribution to discuss the Jackknife-Bayesian estimation of the parameters of Poisson distribution under Entropy loss function,Stein loss function,Linex loss function and Weighted balanced entropy loss function.In order to explore the properties of the Jackknife-Bayesian estimation,it is proved that the Jackknife-Bayesian estimation of Poisson distribution parameters is asymptotically unbiased estimation and asymptotically normal properties under the Entropy loss function.In order to more intuitively reflect the estimation effect,this paper uses MATLAB software to write a program,under different loss functions,to carry out numerical simulation of the Jackknife-Bayesian estimation of the parameters of Poisson distribution,and analyze the simulation results.