Variable Selection For Varying Coefficient Partially Linear Model

With the development of the data storage technology, multi-dimensional data is being processed more often. Hastie and Tibshirani first proposed varying coefficient model y=XTθ(u)+ε which is a powerful tool when deal with high dimensional data. It's a relatively new direction in the area of high-dimensional regression. This thesis is dedicated on how to choose variable in the varying coefficient model y=XTθ(u)+ε. The significant variable will be selected out and also estimate the accordingly functional coefficientθ(·).This thesis utilize SCAD as a penal factor and use B-spline to fit the functional coefficientθ(·). In the first step, use local polynomial to get the estimation of f(xi),i=1,...,n, then put them into the penalty function. Meanwhile minimize the objective function of the two methods in order to select variable. Also the functional coefficient will be derived. A lot of simulation work has been done to check the estimation method and after the simulation, it is showed that this method has good ability in variable selection.