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应用数学学报  1993, Vol. 16 Issue (4): 544-559    DOI:
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经验过程一致偏差概率的指数界及其应用(Ⅰ)
朱力行, 张健, 成平
中国科学院系统科学研究所, 北京 100080
THE EXPONENTIAL BOUNDS FOR THE UNIFORM DEVIATION PROBABILITIES OF EMPIRICAL PROCESSES WITH THEIR APPLICATIONS (Ⅰ)
ZHU LI-XING, ZHANO JIAN, CHENG PING
Institute of System Sciences, Academia Sinica, Beijing 100080
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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-S拟合优度检验).
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朱力行
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Abstract: Suppose that X1,…,Xn are the independent d-dimensional random vectors. In this paper 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 repeated chain method, randomization method and symmetrization method to derive the exponential bounds which are close to the optimal bounds. As an application, we investigate the Projection Pursuit problems.
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收稿日期: 1990-07-18;
引用本文:   
朱力行,张健,成平. 经验过程一致偏差概率的指数界及其应用(Ⅰ)[J]. 应用数学学报, 1993, 16(4): 544-559.
ZHU LI-XING,ZHANO JIAN,CHENG PING. THE EXPONENTIAL BOUNDS FOR THE UNIFORM DEVIATION PROBABILITIES OF EMPIRICAL PROCESSES WITH THEIR APPLICATIONS (Ⅰ)[J]. Acta Mathematicae Applicatae Sinica, 1993, 16(4): 544-559.
 
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