您的位置:山东大学 -> 科技期刊社 -> 《山东大学学报(理学版)》

《山东大学学报(理学版)》 ›› 2026, Vol. 61 ›› Issue (9): 123-130.doi: 10.6040/j.issn.1671-9352.0.2024.099

• • 上一篇    

独立同分布序列均值渐变模型的Ratio检验

郑冬雪1,魏岳嵩1*,许天明2   

  1. 1.淮北师范大学数学与统计学院, 安徽 淮北 235000;2.浙江工商大学统计与数学学院, 浙江 杭州 310018
  • 发布日期:2026-09-30
  • 通讯作者: 魏岳嵩(1975— ),男,教授,博士,研究方向为时间序列分析. E-mail:wysxjtu@163.com
  • 作者简介:郑冬雪(1999— ),女,硕士研究生,研究方向为时间序列分析. E-mail:2075187953@qq.com *通信作者:魏岳嵩(1975— ),男,教授,博士,研究方向为时间序列分析. E-mail:wysxjtu@163.com
  • 基金资助:
    安徽省自然科学基金资助项目(1908085MF186);安徽省高等学校自然科学基金资助项目(KJ2020A0024);安徽省新时代育人质量工程项目(Anhuineweraeducationqualityproject:2023yjsxxsfkc027)

Ratio test for the mean gradual model of an independent identically distributed sequence

ZHENG Dongxue1, WEI Yuesong1*, XU Tianming2   

  1. 1. School of Mathematics and Statistics, Huaibei Normal University, Huaibei 235000, Anhui, China;
    2. School of Statistics and Mathematics, Zhejiang Gongshang University, Hangzhou 310018, Zhejiang, China
  • Published:2026-09-30

摘要: 针对随机误差项是独立同分布序列的均值渐变模型中可能存在的变点问题,提出一种改进的Ratio检验统计量来检验变点的存在性,并得到Ratio检验统计量在原假设和备择假设下的极限分布。最后,通过数值模拟和实证分析说明Ratio检验法的有效性。

关键词: 均值渐变模型, Ratio统计量, 极限分布, Monte Carlo方法

Abstract: In view of the possible change point problem in the random error term from an independent identically distributed sequence, an improved Ratio test statistic is proposed to test the existence of change points, and the limit distributions of the Ratio test statistic under the null hypothesis and alternative assumptions are also obtained. Finally, the effectiveness of the Ratio method is illustrated by numerical simulation and empirical analysis of instances.

Key words: mean gradual model, Ratio statistic, limit distribution, Monte Carlo method

中图分类号: 

  • O211.1
[1] Page E S. Continuous inspection schemes[J]. Biometrika, 1954, 41(1/2): 100-115.
[2] Pepelyshev A, Polunchenko A S. Real-time financial surveillance via quickest change-point detection methods[J]. Statistics and its Interface, 2017, 10: 93-106.
[3] Jiang Feiyu, Zhao Zifeng, Shao Xiaofeng. Time series analysis of COVID-19 infection curve: a change-point perspective[J]. Journal of Econometrics, 2023, 232(1): 1-17.
[4] Punt A E, Szuwalski C S, Stockhausen W. An evaluation of stock-recruitment proxies and environmental change points for implementing the US sustainable Fisheries act[J]. Fisheries Research, 2014, 157: 28-40.
[5] Jarušková D. Testing appearance of linear trend[J]. Journal of Statistical Planning and Inference, 1998, 70(2): 263-276.
[6] Madurkayová B. Ratio tests for gradual changes[C] //WDS'07 Proceedings of Contributed Papers: Part I-Mathematics and Computer Sciences, 2007: 175-180.
[7] 赵文芝, 任肖霖. 长相依均值渐变模型的Ratio检验[J]. 西北大学学报(自然科学版), 2018, 48(6): 797-802. Zhao Wenzhi, Ren Xiaolin. Ratio test for gradual change in the mean of long memory sequence[J]. Journal of Northwestern University(Natural Science Edition), 2018, 48(6): 797-802.
[8] 金浩, 高奎, 张思. 基于Bootstrap方法的重尾相依序列均值变点Ratio检验[J]. 统计与决策, 2019, 35(23): 11-16. Jin Hao, Gao Kui, Zhang Si. Ratio tests for mean break with heavy-tailed dependent sequence based on bootstrap method[J]. Statistics and Decision, 2019, 35(23): 11-16.
[9] 赵文芝, 吕会琴. 厚尾相依序列均值变点Ratio检验[J]. 山西大学学报(自然科学版), 2016, 39(3): 410-414. Zhao Wenzhi, Lyu Huiqin. Ratio test for change point in the mean of heavy-tailed dependent sequence[J]. Journal of Shanxi University(Natural Science Edition), 2016, 39(3): 410-414.
[10] 乔瑞, 杨云峰, 金浩. 基于Bootstrap方法的厚尾AR(p)序列均值变点检验[J]. 昆明理工大学学报(自然科学版), 2022, 47(2): 175-184. Qiao Rui, Yang Yunfeng, Jin Hao. Bootstrap procedures for mean change point detection in AR(p)heavy-tailed series[J]. Journal of Kunming University of Science and Technology(Natural Science Edition), 2022, 47(2): 175-184.
[11] Hušková M. Gradual changes versus abrupt changes[J]. Journal of Statistical Planning and Inference, 1999, 76(1/2): 109-125.
[12] Hušková M. Estimators in the location model with gradual changes[J]. Commentationes Mathematicae Universitatis Carolinae, 1998, 39(1): 147-157.
[13] Ding Saisai, Li Xiaoqin, Yang Wenzhi, et al. The consistency of the CUSUM-type estimator of the change-point and its application[J]. Mathematics, 2020, 8(12): 2113-2124.
[14] Ding Saisai, Fang Hongyan, Dong Xiang, et al. The CUSUM statistics of change-point models based on dependent sequences[J]. Journal of Applied Statistics, 2022, 49(10): 2593-2611.
[15] Koronacki J, Csörgö M, Révész P. Strong approximations in probability and statistics[J]. Mathematica Applicanda, 1983, 11(23): 77-87.
[16] Hušková M, Steinebach J. Limit theorems for a class of tests of gradual changes[J]. Journal of Statistical Planning and Inference, 2000, 89(1/2): 57-77.
[17] Horváth L, Horváth Z, Hušková M. Ratio tests for change point detection[J]. IMS Collections, 2008, 1: 293-304.
[1] 李小娟,高强. 次线性期望框架下乘积空间的正则性[J]. 山东大学学报(理学版), 2018, 53(4): 66-75.
Viewed
Full text


Abstract

Cited

  Shared   
  Discussed   
No Suggested Reading articles found!