Variable Selection In Additive Model With Measurement Error

In general regression models,it is usually assumed that there is no errors in the observa-tions of explanatory variables.However,in practical problems in many fields,explanatory variables often contain measurement errors.If we neglect the influence of measurement error,it may cause a huge deviation in statistical inference,and the conclusions obtained can be quite different from the actual situation.Therefore,in recent years,the research on measurement error has received extensive attention.On the other hand,the additive model can be applied to many types of problems because of its flexibility that the model is not limited by the function form.The focus of this article is to consider how to perform model estimation and variable selection when measurement error problem shows up under the framework of the additive model.First,based on current research,I shortly summarize the basic concepts and basic methods of measurement error model,and then introduce the penalized least square dealing with partial linear measurement error model.In order to develop this idea,I summarize the theoretical basis of B-spline and group variable selection method,and use them in additive model with measurement error.The B-spline is used in transforming nonparametric model into a linear one,and the adjusted least square is used to construct the new objective function.To simplify the problem,I redefine the variables and use Taylor's expansion to complete the derivation and the calibration of measurement error.At last,group selection penalty is added to select important variables and coordinate descent is used to calculate.Then by doing a series of simulation study,I make comparison on the prediction error and variable selection accuracy between the models whether or not dealing with measurement error,and the models using different group variable selection methods,in the situations whether the independent variables have self-correlation and the dependent variable is sen-sitive to the changes of the independent variables or not.The result of simulation shows that when using calibration and group variable selection method proposed from this article to deal with the measurement error and variable selection problem in the additive model,the estimation accuracy of the model is improved.At the same time it is helpful to choose the effective variables correctly and eliminate the irrelevant variables.Meanwhile,group SCAD behaves better than group Lasso on the whole.In the end,the method is applied on a real data which contains measurement error.The additive model of calories from fat on several independent variables is established while selecting important variables.