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中国工业与应用数学学会会刊
主管：中华人民共和国教育部
主办：西安交通大学
ISSN 1005-3085  CN 61-1269/O1
工程数学学报

工程数学学报 ›› 2019, Vol. 36 ›› Issue (6): 637-646.doi: 10.3969/j.issn.1005-3085.2019.06.003

• • 上一篇    下一篇

线性模型中基于加权残差的渐进变点检测

赵文芝1, 夏志明2   

  1. 1- 西安工程大学理学院，西安 710048
    2- 西北大学数学学院，西安 710069
  • 收稿日期:2017-09-30 接受日期:2019-03-19 出版日期:2019-12-15 发布日期:2020-02-15
  • 通讯作者: 夏志明 E-mail: statxzm@nwu.edu.cn
  • 基金资助:
    国家自然科学基金(11771353).

Weighted-residual Based Detection Methods for Gradual Structure-changes in Linear Models

ZHAO Wen-zhi1, XIA Zhi-ming2   

  1. 1- School of Science, Xi'an Polytechnic University, Xi'an 710048
    2- School of Mathematics, Northwest University, Xi'an 710069
  • Received:2017-09-30 Accepted:2019-03-19 Online:2019-12-15 Published:2020-02-15
  • Contact: Z. Xia. E-mail address: statxzm@nwu.edu.cn
  • Supported by:
    The National Natural Science Foundation of China (11771353).

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摘要： 本文研究线性模型中渐变变点的检验问题．首先，提出了基于加权残差部分和Weighted-CUSUM的检验统计量．其次，证明了原假设下检验统计量依分布收敛于标准布朗桥，备择假设下检验统计量依分布收敛于带有漂移项的布朗桥，并给出检验相合性的条件．最后，模拟结果表明所提方法是可行的．

关键词: 渐变变点, Weighted-CUSUM, 线性模型, 布朗桥, 相合性

Abstract: In this paper, we study how to detect gradual changes in linear models. Firstly, the test statistics based on the weighted residual part and the weighted-CUSUM are proposed. Secondly, it is proved that the test statistics converge in distribution to the standard Brownian bridge under the original assumption, converge in distribution to the Brownian bridge with a drift term under the alternative hypothesis. The conditions for the test consistence are also given. Finally, simulation results show that the proposed method is feasible.

Key words: gradual change in structure, Weighted-CUSUM, linear models, Brownian bridge, consistency

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