Biological movement patterns can sometimes be quasi linear with abrupt changes in direction and speed, as in plastids in root cells investigated here. For the analysis of such changes we propose a new stochastic model for movement along linear structures. Maximum likelihood estimators are provided, and due to serial dependencies of increments, the classical MOSUM statistic is replaced by a moving kernel estimator. Convergence of the resulting difference process and strong consistency of the variance estimator are shown. We estimate the change points and propose a graphical technique to distinguish between change points in movement direction and speed.

翻译：生物运动模式有时呈现准线性特征，并伴随方向和速度的突然变化，正如本文所研究的根细胞质体运动。为分析此类变化，我们提出了一种新的线性结构运动随机模型。该模型给出了极大似然估计量，并针对增量序列相关性，采用移动核估计器替代传统MOSUM统计量。证明了所得差值过程的收敛性以及方差估计量的强相合性。我们估算变化点，并提出一种图形化方法来区分运动方向和速度的变化点。