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Title: Dynamical segmentation of a functional data sequence Authors:  Jeng-Min Chiou - Academia Sinica (Taiwan) [presenting]
Yu-Ting Chen - National Chengchi University (Taiwan)
Abstract: A two-stage approach is presented to detect multiple changes in the mean functions of a functional data sequence with an application to road traffic segmentation. The optimality of the segmentation is characterized by minimizing the trace of a covariance operator of the random functions restricted to an $L_2$ subspace. The aim is to estimate the unknown number and positions of the change points that define the segments. The method first searches for change points recursively with a prespecified number using the optimal segmentation criterion, and then ascertain these to be the change points by backward elimination using hypotheses testing on the covariance operators. We present the consistency result of the algorithm in identifying multiple change points. We examine its practical performance through a simulation study under various scenarios of the total number along with the positions of the change points and apply the method to segmentation of freeway traffic conditions.