回归函数的投影寻踪逼近的L_p收敛性

The L_p Convergence for Projection Pursuit Regression

投影寻踪是用来处理高维数据得一类新型统计方法．由于不知道Ｅ（ｒｍ（ｘ）｜ａＴｍｘ）的具体形式，给投影寻踪回归的应用带来一定的困难，为此，作者曾证明岭函数为多项式形式的投影寻踪回归的 Ｌ２收敛性［３］，本文在文献 ［３］的基础上进一步证明了回归函数投影寻踪逼近的 Ｌｐ收敛性．

Projection Pursuit (PP) is a new statistical method which can be used to handle with high- dimensional data. However, no specific forms of the ridge function for projection pursuit regression (PPR) have been proposed, so it is difficult to employ the PPR to solve practical problems. The authors have proposed polynomials as ridge function and proved the L2 convergence for PPR [3]. Furthermore, we prove the Lp convergence of projection pursuit approximation for regression function in this paper.