Research On Several Kinds Of The First-order Approximated Jackknifed Estimators In Binary Logistic Regression Model

The binary logistic regression model is an important kind of statistical model in the generalized linear model,and commonly used to statistical analysis in the fields of biological statistics,criminology and sociology,etc,and it is one of the model which has been widely applied in modern statistics.It is great significance to the study of parameter estimator in this model.The common parameter estimator method in this model is maximum likelihood estimator.However,when the explanatory variables in the model have multicollinearity,the asymptotic mean square error of the maximum likelihood estimation will become larger.Therefore,relevant scholars have proposed some improved estimators as alternative estimators for the maximum likelihood estimator,such as logistic regression ridge estimator etc.In this paper,aiming at the problem of multicollinearity existing in the model,combines the jackknife method and some existing estimator methods,put forward and discuss the superiority of several types of new estimators.Firstly,it introduces the research status of the binary logistic regression model and parameter estimator at home and abroad,and the innovations of this paper.Secondly,combining jackknife method and (?)zkale’s first-order approximated Liu estimator,a new kind of estimation method,namely first-order approximated jackknifed Liu estimator,is proposed.The optimization and goodness of the new estimator is discussed in the sense of bias,mean square error matrix or mean square error.Furthermore,Combined with jackknife method and (?)zkale’s first-order approximated two-parameter estimator,a new class of estimation method,namely firstorder approximated jackknifed two-parameter estimator,is proposed.Get the the new estimator bias is less than biases of the first-order approximated two-parameter estimator,the first-order approximated jackknifed ridge estimator and the first-order approximated ridge estimator.Under the mean square error matrix and the mean square error criterion,the the sufficient or necessary and sufficient conditions of the new estimator are superior to other estimators.Then based on Monte Carlo simulation and empirical analysis methods,the nature of the new estimator is explained.Once again,According to Taylor series,differential mean value theorem and the maximum likelihood method,get a first-order approximated Liu-Type estimator.Then,combined with the first-order approximated Liu-Type estimator and the jackknife method,proposed a new estimation method is the first-order approximated jackknifed Liu-Type estimator.At the same time,based on theoretical research,Monte Carlo simulation and empirical analysis method,the performance of the first-order approximated jackknifed Liu-type estimator is verified in the sense of bias,mean square error matrix and mean square error.Finally,the research results of this article are summarized,and some thoughts and suggestions are given for future research work.