Das Ritabrata, Banerjee Moulinath, Nan Bin, Zheng Huiyong
Department of Biostatistics, University of Michigan, Ann Arbor, MI 48109 (
Department of Statistics, University of Michigan, Ann Arbor, MI 48109 (
J Am Stat Assoc. 2016;111(515):1132-1143. doi: 10.1080/01621459.2015.1073154. Epub 2016 Oct 18.
Estimation of change-point locations in the broken-stick model has significant applications in modeling important biological phenomena. In this article we present a computationally economical likelihood-based approach for estimating change-point(s) efficiently in both cross-sectional and longitudinal settings. Our method, based on local smoothing in a shrinking neighborhood of each change-point, is shown via simulations to be computationally more viable than existing methods that rely on search procedures, with dramatic gains in the multiple change-point case. The proposed estimates are shown to have [Formula: see text]-consistency and asymptotic normality - in particular, they are asymptotically efficient in the cross-sectional setting - allowing us to provide meaningful statistical inference. As our primary and motivating (longitudinal) application, we study the Michigan Bone Health and Metabolism Study cohort data to describe patterns of change in log estradiol levels, before and after the final menstrual period, for which a two change-point broken stick model appears to be a good fit. We also illustrate our method on a plant growth data set in the cross-sectional setting.
在折断棍模型中估计变化点位置在对重要生物学现象进行建模方面具有重要应用。在本文中，我们提出了一种基于似然性的计算经济方法，用于在横断面和纵向设置中有效地估计变化点。我们的方法基于在每个变化点的收缩邻域内进行局部平滑，通过模拟表明，与依赖搜索程序的现有方法相比，它在计算上更可行，在多个变化点的情况下有显著提升。所提出的估计量被证明具有[公式：见正文]一致性和渐近正态性——特别是，它们在横断面设置中是渐近有效的——这使我们能够提供有意义的统计推断。作为我们主要的、具有启发性的（纵向）应用，我们研究了密歇根骨健康与代谢研究队列数据，以描述末次月经前后对数雌二醇水平的变化模式，对于该数据，两变化点折断棍模型似乎是一个很好的拟合。我们还在横断面设置的植物生长数据集上说明了我们的方法。
