论文标题
在高维数据中约会中断
Dating the Break in High-dimensional Data
论文作者
论文摘要
本文涉及对独立高维数据平均值的变化点位置的估计和推断。我们的变化点位置估计量最大化了新的基于U统计的目标函数，并且在适当的居中和归一化之后，在轻度假设下获得了其收敛速率和渐近分布。与文献中基于最小二乘相比，我们的估计器的效率更高。基于渐近理论，我们通过插入归一化数量的数量的一致估计来构建置信区间。我们还提供基于自动启动的置信区间，并在适当条件下陈述其渐近有效性。通过仿真研究，与几个现有竞争对手相比，与最小二乘基于平方的对应物相比，我们证明了新变化点位置估计器的有限样本性能以及基于自举的置信区间的有限样本性能。基于高维U统计的渐近理论与文献中开发的理论大不相同，并且具有独立的利益。
This paper is concerned with estimation and inference for the location of a change point in the mean of independent high-dimensional data. Our change point location estimator maximizes a new U-statistic based objective function, and its convergence rate and asymptotic distribution after suitable centering and normalization are obtained under mild assumptions. Our estimator turns out to have better efficiency as compared to the least squares based counterpart in the literature. Based on the asymptotic theory, we construct a confidence interval by plugging in consistent estimates of several quantities in the normalization. We also provide a bootstrap-based confidence interval and state its asymptotic validity under suitable conditions. Through simulation studies, we demonstrate favorable finite sample performance of the new change point location estimator as compared to its least squares based counterpart, and our bootstrap-based confidence intervals, as compared to several existing competitors. The asymptotic theory based on high-dimensional U-statistic is substantially different from those developed in the literature and is of independent interest.
