Research On Parameter Estimation Based On Bootstrap Method

Parameter estimation is an important issue in statistical models because parameter estimation is a prerequisite for predicting dependent variables.The parameter estimation methods used for different statistical models are also different.Therefore,this paper estimates the logistic regression model and the linear regression model based on different bootstrap methods.Through empirical analysis and numerical simulation analysis,the parameters bootstrap,non-parameter bootstrap,parametric Bayes bootstrap and non-parametric Bayes bootstrap are studied respectively.Methods Parameter estimation in logistic regression models,parameter estimation of residual bootstrap,Bayesian residual bootstrap,and Bayesian paired bootstrap method in a linear regression model.And through the comparative analysis of the superiority of several methods.Firstly,for the estimation of regression parameters in Logistic regression model,Bayesian bootstrap estimation method is combined with parameter bootstrap estimation method and non-parameter bootstrap estimation method.Two estimation methods of parameter and non-parametric Bayesian bootstrap are proposed.Based on the standard error,the ratio of the estimated falling interval in a given interval and the length of the confidence interval,the empirical and simulation results show that the stability and accuracy of the parameter Bayesian bootstrap estimation method are better than the maximum likelihood estimation method and the parameters bootstrap.The reliability of the parameters Bayesian bootstrap and the parameters bootstrap method is not significant.In the case of small sample size,the reliability and accuracy of the non-parametric Bayesian bootstrap estimation method are better than the maximum likelihood estimation method.The stability of the non-parametric Bayesian bootstrap estimation method is better than that of the non-parametric bootstrap method.The stability,reliability and accuracy of the parameter Bayesian bootstrap estimation method are better than the non-parametric Bayesian bootstrap estimation method.Secondly,aiming at the estimation of regression parameters in the linear regression model,the Bayesian bootstrap estimation method and the residual bootstrap estimation method are combined with the paired bootstrap estimation method,and the Bayesian residual bootstrap and Bayesian pairing bootstrap are proposed.Estimation method.In the sense of standard error,the proportion of the estimated falling within a given interval and the length of the confidence interval,it is proved by empirical and simulation analysis that in the case of small sample size,considering stability,reliability and accuracy,The Bayesian residual bootstrap,Bayesian pairing bootstrap and residual bootstrap estimation methods are better than the least squares estimation method;when the sample size is large,the Bayesian residual bootstrap and residual bootstrap estimation methods are better than the minimum two.Multiply estimation,the Bayesian pairing bootstrap estimation method is similar to the least squares estimation method.Finally,the research contents and results of this paper are summarized,and some suggestions and expectations are put forward for the follow-up work.