Variance Change Point Detection Under a Smoothly-Changing Mean Trend with Application to Liver Procurement
Variance Change Point Detection Under a Smoothly-Changing Mean Trend with Application to Liver Procurement
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DOI：
10.1080/01621459.2018.1442341
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发表时间：
2019-04-03
影响因子：
3.7
通讯作者：
Robertson, John L.
中科院分区：
文献类型：
--
作者：
Gao, Zhenguo;Shang, Zuofeng;Robertson, John L.
变点分析的文献大多需要数据分布的突然变化，无论是在几个参数或分布作为一个整体。我们感兴趣的情况下，数据的方差可能会有一个显着的跳跃，而平均值以平滑的方式变化。动机是监测器官表面温度的肝脏采集实验。盲目地将现有的方法应用到例子中会产生错误的变点估计，因为平滑变化的均值违反了突变假设。我们提出了一个惩罚加权最小二乘方法与迭代估计过程，集成了方差变点检测和平滑均值函数估计。该过程从一致的初始均值估计开始，忽略方差异质性。给定方差分量，通过平滑样条估计均值函数作为惩罚加权最小二乘的最小值。给定均值函数，我们提出了一个似然比检验统计量来识别方差变化点。检验统计量的零分布与所有参数估计的收敛速度一起导出。仿真结果表明，该方法具有良好的性能。应用分析为表面温度监测无创评估器官存活性提供了数值支持。本文的补充材料可在网上查阅。
Literature on change point analysis mostly requires a sudden change in the data distribution, either in a few parameters or the distribution as a whole. We are interested in the scenario, where the variance of data may make a significant jump while the mean changes in a smooth fashion. The motivation is a liver procurement experiment monitoring organ surface temperature. Blindly applying the existing methods to the example can yield erroneous change point estimates since the smoothly changing mean violates the sudden-change assumption. We propose a penalized weighted least-squares approach with an iterative estimation procedure that integrates variance change point detection and smooth mean function estimation. The procedure starts with a consistent initial mean estimate ignoring the variance heterogeneity. Given the variance components the mean function is estimated by smoothing splines as the minimizer of the penalized weighted least squares. Given the mean function, we propose a likelihood ratio test statistic for identifying the variance change point. The null distribution of the test statistic is derived together with the rates of convergence of all the parameter estimates. Simulations show excellent performance of the proposed method. Application analysis offers numerical support to non invasive organ viability assessment by surface temperature monitoring. Supplementary materials for this article are available online.