论文标题
高维线性模型的更改点检测：一种通用的尾巴自适应方法
Change Point Detection for High-dimensional Linear Models: A General Tail-adaptive Approach
论文作者
论文摘要
我们提出了一种新的方法，用于检测高维线性回归模型中的变化点。与以前依赖严格的高斯/下高斯错误假设并具有更改点知识的研究不同，我们提出了一种用于变更点检测和估计的尾随自适应方法。我们使用复合分位数和最小平方损耗的加权组合来构建新的损失函数，从而使我们能够从条件均值和分位数中利用信息。对于变更点测试，我们开发了一个具有不同权重的个体测试统计量家庭，以说明未知的尾巴结构。这些单独的测试进一步汇总，以构建强大的尾巴自适应测试，以进行稀疏回归系数变化。为了估算变化点的估计，我们提出了一个基于Argmax的单个估计器家族。我们为这些测试的有效性和变化点估计器提供了理论上的理由。此外，我们引入了一种新算法，用于使用野生二进制分段以尾随的方式检测多个变化点。广泛的数值结果显示了我们方法的有效性。最后，开发了一个称为``tailAdaptiveCpt''的R软件包来实现我们的算法。
We propose a novel approach for detecting change points in high-dimensional linear regression models. Unlike previous research that relied on strict Gaussian/sub-Gaussian error assumptions and had prior knowledge of change points, we propose a tail-adaptive method for change point detection and estimation. We use a weighted combination of composite quantile and least squared losses to build a new loss function, allowing us to leverage information from both conditional means and quantiles. For change point testing, we develop a family of individual testing statistics with different weights to account for unknown tail structures. These individual tests are further aggregated to construct a powerful tail-adaptive test for sparse regression coefficient changes. For change point estimation, we propose a family of argmax-based individual estimators. We provide theoretical justifications for the validity of these tests and change point estimators. Additionally, we introduce a new algorithm for detecting multiple change points in a tail-adaptive manner using the wild binary segmentation. Extensive numerical results show the effectiveness of our method. Lastly, an R package called ``TailAdaptiveCpt" is developed to implement our algorithms.
