一种基于递归残差的回归模型变点检验  

A Test for a Change in Regression Model Based on Recursive Residuals

作　　者：秦瑞兵[1] 赵姣 QIN Ruibing;ZHAO Jiao(School of Mathematical Sciences,Shanxi University,Taiyuan 030006,China)

机构地区：[1]山西大学数学科学学院,山西太原030006

出　　处：《山西大学学报（自然科学版）》2022年第2期363-368,共6页Journal of Shanxi University(Natural Science Edition)

基　　金：山西省自然科学基金(201801D121005);青海省自然科学基金(2019-ZJ-920)。

摘　　要：针对线性回归模型系数向量的变点问题,文章基于递归回归残差平方序列的部分和之比,构造了一种检验方法。在原假设下,得到其渐近分布为维纳过程的泛函,并在备择假设下,证明了该检验方法的发散速度及其渐近发散极限,从而保证了该检验的一致性。模拟表明,本方法在变点发生时刻靠前时的功效具有较大改进,在其他情形与经典的CUSQ检验方法接近。This paper introduced a new approach to test for a change point of the coefficient in a linear regression model based on the ratio of the sum of the squares of recursive regression residuals.The asymptotic distribution of the proposed statisticsis is established under the null hypothesis and it is a functional of a Wiener process,and the divergence velocity and asymptotic divergence limit of the test are provided under the alternative hypothesis,which ensures the consistency of the test.The simulation results show that the proposed method is more powerful than the existing CUSQ test in the case where the change happens in an early stage.

关 键 词：递归回归残差 变点 线性回归模型 一致性 

分 类 号：O212[理学—概率论与数理统计]