Fiducial Inference Of Logistic Regression

Logical regression has been widely used in many fields.Generally,the maximum likelihood estimation method is used to deal with it.At the same time,the Bayesian method can improve the accuracy of logical regression,because the introduction of a reasonable prior distribution function can effectively reduce the errors in estimating parameters.But Fisher put forward the idea of Fiducial inference in 1930,which can estimate parameters without prior information,making parameter estimation simpler.This paper focuses on the Fiducial inference of logistic regression,constructs the confidence interval of logistic regression parameters by Monte Carlo method,and further studies and verifies the Fiducial inference of logistic regression.Firstly,this paper gives the introduction of logical regression,Bayesian and Fiducial inference.Secondly,a limited sample behavior study on logistic regression is conducted based on Fiducial inference,by using control variable method,respectively,simulation comparison of the logistic regression of maximum likelihood estimation,bayesian inference,and Fiducial inference get the confidence interval of regression parameters of coverage,the average length of the confidence interval and the variance,and the Bias and MSE of the estimated parameters.The results show that the results obtained by logistic regression Fiducial inference under the condition of small samples are better than those obtained by other two methods,specifically,the coverage is closer to the given confidence level,the length of confidence interval is narrower under the same confidence level,the Bias and MSE of parameter estimation are smaller,and the accuracy of estimation is higher.Finally,the results of Fiducial inference of logistic regression in different cases are compared separately.According to the numerical simulation results,the Fiducial inference of logistic regression has good properties in the case of small samples.And the empirical research is carried out.