线性模型中基于加权残差的渐进变点检测  

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

作　　者：赵文芝[1] 夏志明 ZHAO Wen-zhi;XIA Zhi-ming(School of Science,Xi’an Polytechnic University,Xi’an 710048;School of Mathematics,Northwest University,Xi’an 710069)

机构地区：[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

出　　处：《工程数学学报》2019年第6期637-646,共10页Chinese Journal of Engineering Mathematics

基　　金：国家自然科学基金(11771353)~~

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.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.

关 键 词：渐变变点 Weighted-CUSUM 线性模型 布朗桥 相合性 

分 类 号：O212.1[理学—概率论与数理统计]