We propose the Multiple Changepoint Isolation (MCI) method for detecting multiple changes in the mean and covariance of a functional process. We first introduce a pair of projections to represent the variability "between" and "within" the functional observations. We then present an augmented fused lasso procedure to split the projections into multiple regions robustly. These regions act to isolate each changepoint away from the others so that the powerful univariate CUSUM statistic can be applied region-wise to identify the changepoints. Simulations show that our method accurately detects the number and locations of changepoints under many different scenarios. These include light and heavy tailed data, data with symmetric and skewed distributions, sparsely and densely sampled changepoints, and mean and covariance changes. We show that our method outperforms a recent multiple functional changepoint detector and several univariate changepoint detectors applied to our proposed projections. We also show that MCI is more robust than existing approaches and scales linearly with sample size. Finally, we demonstrate our method on a large time series of water vapor mixing ratio profiles from atmospheric emitted radiance interferometer measurements.
翻译:我们建议多变点隔离法(MCI) 用于检测功能过程平均值和变量的多重变化。 我们首先引入一对预测, 以代表功能观测“ 之间” 和“ 内部” 的变异性。 然后我们展示一个强化的导合拉索程序, 将预测强有力地分解到多个区域。 这些区域的行为是将每个变化点与其它区域隔离开来, 这样强大的单变点 CUSUM 统计数据可以在区域间应用, 以辨别变化点。 模拟显示我们的方法准确检测了许多不同情景下的变化点的数量和位置。 其中包括光和重尾部数据、 有对称和偏差分布的数据、 分散和密集抽样的变化点数据, 以及平均值和共变性变化。 我们显示, 我们的方法超越了一个最近的多功能变点探测器和数个单变点检测器, 用于我们提议的预测。 我们还表明, MCI 比现有的方法和线性尺度比样本大小的尺度要强。 最后, 我们展示了我们从大气气压内部测量大量时间序列中测量水气压混合比例的方法。