Inference on the Change Point under a High Dimensional Covariance Shift
Inference on the Change Point under a High Dimensional Covariance Shift
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发表时间：
2023
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通讯作者：
A. Kaul;Hongjin Zhang;K. Tsampourakis;G. Michailidis
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作者：
A. Kaul;Hongjin Zhang;K. Tsampourakis;G. Michailidis
我们考虑在高维协方差平移设置中为变化点构建渐近有效置信区间的问题。开发了一种新颖的变点参数估计器，并获得了其在高维尺度下的渐近分布。我们确定所提出的估计器表现出急剧的 Op(ψ -2) 收敛率，其中 ψ 表示变化点之前和之后模型参数之间的跳跃大小。此外，还描述了跳跃大小的消失和非消失状态下渐近分布的形式。在前一种情况下，它对应于不对称布朗运动的 argmax，而在后一种情况下，它对应于不对称随机游走的 argmax。然后，我们获得这些分布之间的关系，从而允许构建机制（消失与非消失）自适应置信区间。为所提出的方法开发了易于实现的算法，并在合成和真实数据集上说明了它们的性能。
We consider the problem of constructing asymptotically valid confidence intervals for the change point in a high-dimensional covariance shift setting. A novel estimator for the change point parameter is developed, and its asymptotic distribution under high dimensional scaling obtained. We establish that the proposed estimator exhibits a sharp Op(ψ −2) rate of convergence, wherein ψ represents the jump size between model parameters before and after the change point. Further, the form of the asymptotic distributions under both a vanishing and a non-vanishing regime of the jump size are characterized. In the former case, it corresponds to the argmax of an asymmetric Brownian motion, while in the latter case to the argmax of an asymmetric random walk. We then obtain the relationship between these distributions, which allows construction of regime (vanishing vs non-vanishing) adaptive confidence intervals. Easy to implement algorithms for the proposed methodology are developed and their performance illustrated on synthetic and real data sets.