基于平滑样条回归的方差变点检测模型  

Variance Variable-point Detection Model Based on Smooth Spline Regression

作　　者：李扬 胡尧 杨超[1] Li Yang;Hu Yao;Yang Chao(School of Mathematics and Statistics,Guizhou University,Guiyang 550025,China;Guizhou Key Laboratory of Public Big Data,Guizhou University,Guiyang 550025,China)

机构地区：[1]贵州大学数学与统计学院,贵阳550025 [2]贵州大学贵州省公共大数据重点实验室,贵阳550025

出　　处：《统计与决策》2020年第14期15-19,共5页Statistics & Decision

基　　金：国家自然科学基金资助项目(11661018);贵州省科技计划项目(黔科合平台人才[2017]5788号)。

摘　　要：文章对均值函数是平稳变化而方差存在显著跳跃情形的数据进行探究,首先同时考虑曲线的拟合优度和粗糙惩罚度,通过广义交叉验证对光滑参数自动搜索,然后利用平滑样条构造惩罚最小二乘对均值函数进行估计,进一步对去均值趋势的残差序列构建似然比检验统计量检测存在的方差变点,并结合二分法对多变点情形进行估计。数值模拟表明,平滑样条估计均值函数拟合效果较好,对方差变点发生位置和变点前后方差的估计也较准确,随样本量的增大,估计的精确度及变点检测功效也随之提高。最后通过实例分析进一步说明了方法的有效性。This paper studies the data that the mean function is a smooth change and the variance has significant jumps.Firstly,both the goodness of fit and the degree of roughness penalty of the curve are considered,and the smooth parameters are searched automatically by generalized cross validation.Then the mean function is estimated by using smooth spline to construct penalty least squares.Furthermore,the variance changing points existing in statistics detection is tested by constructing the likelihood ratio for the residuals of the mean removal trend,and the dichotomy is employed to estimate the multivariate point situation.Numerical simulation shows that the smooth spline estimation mean function has better fitting effect,with relatively more accurate estimation on the location of the variance changing point and the variance before and after the changing point,and that with the increase of sample size,the accuracy of estimation and the efficiency of variable point detection are also improved.Finally,an example is given to illustrate the effectiveness of the method.

关 键 词：惩罚最小二乘 平滑样条 均值函数平稳变化 方差变点 

分 类 号：O212[理学—概率论与数理统计]