经验过程一致偏差概率的指数界及其应用(Ⅰ)  

THE EXPONENTIAL BOUNDS FOR THE UNIFORM DEVIATION PROBABILITIES OF EMPIRICAL PROCESSES WITH THEIR APPLICATIONS (Ⅰ)

作　　者：朱力行[1] 张健[1] 成平[1] 

机构地区：[1]中国科学院系统科学研究所

出　　处：《应用数学学报》1993年第4期544-559,共16页Acta Mathematicae Applicatae Sinica

摘　　要：研究文中问题的诱因是考虑PP型Kolmogorov-Smirnov拟合优度检验问题(简称K-SSuppose that X_1,…, X_n are the independent d-dimensional random vectors. In thispaper we consider the empirical processes, which are constructed by the random vectors,and indexed by the classes of functions with polynomial discrimination. We use the repeatedchain method, randomization method and symmetrization method to derive the exponen-tial bounds which are close to the optimal bounds. As an application, we investigate theProjection Pursuit problems.

关 键 词：经验过程 拟合优度检验 概率测度 

分 类 号：O212.1[理学—概率论与数理统计]