On the Approximation of Quantile Processes by Kiefer Processes

被引：0
|
作者：
Paul Deheuvels
机构：
来源：
Journal of Theoretical Probability | 1998年 / 11卷
关键词：
Empirical processes; quantile processes; order statistics; law of iterated logarithm; almost sure convergence; strong laws; strong invariance principles; strong approximation; Kiefer processes; Wiener processes;
D O I：
暂无
中图分类号：
学科分类号：
摘要：
We prove that the best possible almost sure rate of uniform approximation of a uniform quantile process by a normed Kiefer process is O(n−1/4(log n)1/2× (log log n)1/4).
引用
收藏
页码：997 / 1018
页数：21
相关论文
共 50 条
  • [21] Quantile Markov Decision Processes
    Li, Xiaocheng
    Zhong, Huaiyang
    Brandeau, Margaret L.
    OPERATIONS RESEARCH, 2021, 70 (03) : 1428 - 1447
  • [22] BAHADUR-KIEFER THEOREMS FOR UNIFORM SPACINGS PROCESSES
    BEIRLANT, J
    DEHEUVELS, P
    EINMAHL, JHJ
    MASON, DM
    THEORY OF PROBABILITY AND ITS APPLICATIONS, 1991, 36 (04) : 647 - 669
  • [23] Approximation of Hunt processes by multivariate Poisson processes
    Ma, ZM
    Röckner, M
    Sun, W
    ACTA APPLICANDAE MATHEMATICAE, 2000, 63 (1-3) : 233 - 243
  • [24] Approximation of Markov Processes by Lower Dimensional Processes
    Tzortzis, Ioannis
    Charalambous, Charalambos D.
    Charalambous, Themistoklis
    Hadjicostis, Christoforos N.
    Johansson, Mikael
    2014 IEEE 53RD ANNUAL CONFERENCE ON DECISION AND CONTROL (CDC), 2014, : 4441 - 4446
  • [25] Approximation of Hunt Processes by Multivariate Poisson Processes
    Zhi-Ming Michael Ma
    Wei Sun
    Acta Applicandae Mathematica, 2000, 63 : 233 - 243
  • [26] ON THE APPROXIMATION OF RANDOM-PROCESSES BY CONVOLUTION PROCESSES
    SPLETTSTOSSER, W
    ZEITSCHRIFT FUR ANGEWANDTE MATHEMATIK UND MECHANIK, 1981, 61 (06): : 235 - 241
  • [27] On the local oscillations of empirical and quantile processes
    Deheuvels, P
    ASYMPTOTIC METHODS IN PROBABILITY AND STATISTICS: A VOLUME IN HONOUR OF MIKLOS CSORGO, 1998, : 127 - 134
  • [28] Quantile Processes in the Presence of Auxiliary Information
    Biao Zhang
    Annals of the Institute of Statistical Mathematics, 1997, 49 : 35 - 55
  • [29] CONVERGENCE OF QUANTILE AND SPACINGS PROCESSES WITH APPLICATIONS
    SHORACK, GR
    ANNALS OF MATHEMATICAL STATISTICS, 1972, 43 (05): : 1400 - &
  • [30] Quantile processes in the presence of auxiliary information
    Zhang, B
    ANNALS OF THE INSTITUTE OF STATISTICAL MATHEMATICS, 1997, 49 (01) : 35 - 55
12345