Adaptive Spline Lasso Based On Local Penalty

Regression analysis is a statistical tool for studying dependent relation-ship between variables. It contains parametric regression and nonparametric regression. The parametric regression method needs a prior assumption on the form of regression function, however, which will lead to the fault of model’s construction in some cases. Nonparametric regression needs no such prior as-sumption, which is a data driven method to decide the regression function to fit the data. It can improve the accuracy of fit. In the case of high dimen-sional data, it is an important work to select appropriate variables for model’s analysis. Lasso is one of the most commonly used tools based on penalized regression.This paper firstly introduces the construction of regression model based on truncated power basis penalized spline in detail. An example of integral calculation by penalized regression model is given to present the application value of penalized spline regression. And the fitting of Lorenz curve is also shown by this method. Secondly, after introducing the definition of B spline basis and its properties, one improved Lasso method is studied based on pe-nalized spline regression. The reciprocal of the range of response variable’s data along with the region are utilized to compress the explainable variable’s coefficients. Simulations show that this improved lasso method outperforms the classical Lasso. An application of this method on medical data is shown at last.