The Study Of Parameter Estimation In Logit Model

In recent years, statistics and machine learning have been developed a lot. At the same time, data quantity is growing sharply. As a result, more and more statistical models are largely applied in the field of computer, among which the logit model occupies a more and more important position. In addition, Logit Model in dealing with the economic, financial, speech and image recognition shows good characteristics gradually. Traditionally, we estimate the logit model parameters through a maximum likelihood function based on the sample.The solution stated above has the following limitations. First of all, this method is sensitive to the choice of initial value, since it could not guarantee the global optimal solution; what’s more, the iterative speed and result accuracy are set just by the experience rather than theories. Logit model in related fields has made good results. Therefore, the study of estimating parameters of this model by different methods has a great significance. In addition, this method only use the discrete output to estimate the parameters, ignoring the inner structure of the data. The Logit model has achieved good results in the economic, financial, biological and other fields, so the study of the parameter estimation has great significance.In logit model, the input variables influence the probability of events. For a given input, we can get an output with a certain probability. Thus, we can divide the sample into several groups according to the input of the sample points. Then there will several groups, and every point of the same group has the same input. So we can calculate the frequency of every kind of input. With these information, we can get several equations.Then, we put forward two kinds of methods for estimating parameters in the logit model based on the equation. The first is the least squares method, which is easy to compute. Since frequency is often used to approximate probability, the random test times of each input type must be considered. We introduces the EM algorithm which overcomes this limitation. It proposed an objective function which account for both the test times and the accuracy of the estimation in this iteration. Bigger sample size and less bias make the larger weights in the EM algorithm, which leads a higher speed of convergence. Therefore in the practical application, we can use the three methods to estimate the model parameters, which can be used to deal with various kinds of classification problems better.