线性模型中多变点的置信区间估计  

Confidence Intervals for Multiple Change-Points in Linear Models

作　　者：吕丽 金百锁[1] Lü Li;JIN Baisuo(School of Management,University of Science and Technology of China,Hefei 230026)

机构地区：[1]中国科学技术大学管理学院,合肥230026

出　　处：《系统科学与数学》2021年第8期2310-2326,共17页Journal of Systems Science and Mathematical Sciences

基　　金：国家自然科学基金面上项目(71873128);国家自然科学基金重点项目(71631006);国家自然科学基金创新群体项目(71921001);国家自然科学基金交流项目(72111530199)资助课题;中国科学技术大学创新群体培育项目(WK2040160028)。

摘　　要：基于Jin等(2016)提出的两阶段多变点同时估计方法,文章提出了一种结合随机加权自助法和高斯混合模型得出多变点置信区间的估计方法.使用随机加权自助法能得到变点估计的直方图,然后采用高斯混合模型估计变点的分布.若变点前后参数变化较小,采用随机加权自助法会产生冗余的变点估计,因此文章采用直方图的峰数加一的方法来确定高斯混合模型中的模型个数,这种确定高斯分模型个数的方法能够提高置信区间精度.模拟结果和原油价格道琼斯指数的日交易收盘价数据的实证分析都表明了该研究方法的有效性和准确性.Based on the FTSMCD method(Two stage multiple change points detection) proposed by Jin,et al.(2016),we tackle the problem of constructing changepoints confidence interval estimations in multiple linear regression models.The key idea is to obtain the resampled change-point estimations sequence by using randomly weighted bootstrap method.Using the randomly weighted bootstrap method can get the histogram of the change point estimation,and then we use the Gaussian mixture model to estimate the distribution of the change point.If the parameter changes before and after the change point are small,the randomly weighted bootstrap method will generate redundant change point estimates.Therefore,adding one to the peak number of the histogram is used to determine the number of sub-models in the Gaussian mixture model,which can significantly improve the accuracy of the confidence intervals.Compared with MC simulations,randomly weighted bootstrap simulations perform well and the analysis of weekly NYMEX oil price the daily closing price of the Dow Jones Industrial Average data also reveals the effectiveness of the proposed method.

关 键 词：变点 置信区间 高斯混合模型 随机加权自助法 

分 类 号：O212.1[理学—概率论与数理统计]