Research On Almost Unbiased Ridge Estimation And Outliers Of Semi-varying Coefficient Model

Semi-varying coefficient model has been widely concerned by the relevant scholars because of its own advantages.It has both simple and easy to explain characteristic of the parameter model and flexibility and adaptability of the nonparametric model.At the same time,the "Curse of Dimensionality" of the nonparametric model can be avoided,and the accuracy of model fitting is improved.There are many methods for estimating the constant and variable coefficient functions of semi-varying coefficient model,such as two step estimation method,profile least square method and local linear fitting.These methods provide support for the study of this paper.Firstly,this paper studies the multicollinearity problem of semi-varying coefficient model.That is.the coefficient matrix of the parameter part xT of the model is ill conditioned or non column full rank,which results in the accuracy of the estimated value is worse,and even the previous method can't get the estimated value.To solve this problem,in this paper,the almost unbiased ridge estimation method of semi-varying coefficient model is given for semi-varying coefficient model based on profile least square method and ridge estimation method.It is proved that the almost unbiased ridge estimation is better than ridge estimation from partial and mean square error.It is verified by several numerical simulation experiments.The results show that the almost unbiased ridge estimation method is feasible and practical for semi-varying coefficient model with multicollinearity.Secondly,this paper analyzes the problem of outliers of semi-varying coefficient model.It is common to have outliers in data processing.Because the outliers deviate from the trajectory of the normal data point or different from statistical law of the normal data,it will cause interference to the regression results and make the fitting effect of the models worse.To solve this problem,this paper introduces an indication matrix based on the profile least square method to give an outlier analysis model.The outlier analysis model is applied to analyze and process the data.Based on residual squared sum,LYD test and Cook test method,the judgment method for the existence of outliers in the semi-varying coefficient model and the discrimination method of number and position of outliers are given.And several numerical simulation examples are used to verify the method.The results show that it is feasible and effective to discriminate the outliers of semi-varying coefficient outlier model.