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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)
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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 Suppose 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.
出处 《应用数学学报》 CSCD 北大核心 1993年第4期544-559,共16页 Acta Mathematicae Applicatae Sinica
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