Research On The Maximum Lq Likelihood Estimation Problem Of Logistic Regression Model

In recent years,Logistic regression model has been extensively developed and applied in theory and method.Logistic regression model does not require the data type of the explanatory variable.When the response variable is a categorical variable,the Logistic regression model is commonly used to study the potential relationship between the response variable and the explanatory variable.For the two-category Logistic regression model,when studying the problem of parameter estimation,the commonly used parameter estimation method is the maximum likelihood estimation method.The estimator of maximum likelihood estimation has a good large sample nature,but when the sample size is small,this paper adopts the maximum Lq likelihood estimation method.In practical problems,explanatory variables are prone to multicollinearity.In order to solve such problems,we need to select variables.Therefore,this paper considers the maximum Lq likelihood estimation method with Lasso penalty,and discusses the asymptotic properties of the Lasso maximum Lq likelihood estimator.Under certain regularization conditions,it is proved that the Lasso maximum Lq likelihood estimator satisfies asymptotic normality.In the numerical simulation,the Lasso maximum Lq likelihood estimation method is compared with the existing Lasso maximum likelihood estimation method.And it can be obtained that when the sample size is small or medium,and the optimal q value is selected,the Lasso maximum Lq likelihood is verified compared with the Lasso maximum likelihood estimation,and the estimation has better fitting effect and stronger variable selection ability.When the sample size is large,the two parameter estimation methods also have better performance.Subsequently,the Lasso maximum Lq likelihood estimation method is extended from the two-category Logistic regression model to the multi-category Logistic regression model,and similar conclusions are given.Finally,the selection method of the optimal q value is discussed.And use actual data to compare Lasso maximum likelihood estimation and Lasso maximum Lq likelihood estimation.By comparing the prediction accuracy of the above two parameter estimation methods,it is found that when the optimal q value is selected,the Lasso maximum Lq likelihood performs better than the existing Lasso maximum likelihood estimation.