Logit Model Parameter Estimation And Empirical Study Based On Empirical Likelihood

Generalized linear models emerged as the promotion of classical linear models,it is suitable for continuous data,but also for discrete data particularly(as count data and attribute data).It played an important role in statistical analysis of biological,medical,economic and social data.Depending on the distribution function and the connection function can be subdivided into different models and which is the most widely used is the Logit model.This model can be predicts the probability of a dependent variable in the form of classification for each class occurrence by a set of independent variables.In actual application environment produced a series expansion method which relaxed the basic assumptions of classical Logit model gradually because there are many restrictions in it.In the second chapter we have discussion about the advantages and disadvantages of commonly used models.A major drawback of GLMs,however,is that a full parametric specification of an error distribution for the data is required,a requirement that is too demanding in many applied settings.This article construct Logit model based on empirical likelihood method and try to solve this problem by the feature of the method.The main work of this paper is divided into two parts.The first part has solving Logit model by profile likelihood method after construction the model while get the estimated parameters and distribution of the data simultaneously.The resulting estimators are shown to be consistent and jointly asymptotically normal in distribution.Then use the Monte Carlo method to simulate study under different control conditions,it proves the model of stability and applicability.Finally,using a variety of methods to analysis an actual data,further illustrate the constructed model can indeed be effectively fitting results.The second part is the empirical analysis section about listed companies' financial crisis early warning.Risk in financial crisis is one of the most important risks of corporate risks.The financial situation early-warning early as possible can help enterprises to develop measures and reducing the possibility of financial distress.In this section first we discuss the choice of indicators about representatives of listed companies' financial status.Collect the data of ST companies in all the A shares,the data should be three years ago before company financial distress.From a financial five aspects level selected 20 financial indicators as a research base.Establishment of early warning model by screening and retain the five independent variables indicators finally.The proposed model performance well by contrast with prediction models which given by same domain articles.The model proposed in this article does not require specification of an error distribution or variance function for the data.The approach involves treating the error distribution as an infinite-dimensional parameter,which is then estimated simultaneously with the mean-model parameters using a maximum empirical likelihood approach.The resulting estimators are shown to be consistent and jointly asymptotically normal in distribution.As can be seen in the simulation study,it does have certain advantages the approach which proposed in this article has a good performance both in accuracy and flexibility.