The Relative Error Estimation Of Parametric And Nonparametric

Least squares estimation in statistics is very important,Especially in the linear model,but in the practical application of reality,Least squares or the minimum absolute error estimation would sometimes unsatisfactory,then we choose the relative error than the absolute error is more meaningful.Parameter estimation and nonparametric estimates are discussed based on the least absolute error.But sometimes we can find the effect is not good,We can put it extended to the absolute minimum relative error or the least square error.One advantage is that they are scale free or unit free.The relative error of the estimated discussion have the following kinds of model and method:Linear model:Nonparameter model: The yi is a nonlinear estimation of yi.Multiplicative model or accelerated failure time model:We find (1.3) has a qualitative leap compared to the (1.1) and (1.2),This is because the second item of the model (1.3) has the unknown parameters.In the next chapters we will presente the reasons and advantages of this model. Inspired by (1.3).We put the model (1.1) and (1.2) to the form of (1.3).The improved linear model:The improved nonparameter model:Here we only give the form of absolute relative error.Through the simu-lation, we found that this model than previous least squares or the minimum relative error estimation will be more precise.