论文标题
具有时间依赖性的高维线性模型的最佳更改点测试
Optimal Change-point Testing for High-dimensional Linear Models with Temporal Dependence
论文作者
论文摘要
在本文中，我们研究了高维线性模型的更改点测试，这是文献中尚未得到很好探讨的重要问题。具体而言，我们提出了一个二次形式累积总和（CUSUM）统计量，以测试高维线性模型中回归系数的稳定性。该测试在任何所需的水平上控制I型误差，并且对时间依赖的观测值是鲁棒的。我们在零假设下建立了其渐近分布，并证明它在多个变更点的替代方案上渐近强大，并为广泛的一系列高维模型实现了最佳检测边界。我们进一步开发了一种自适应程序来估计测试的调整参数，从而使我们的方法在应用中实用。此外，我们扩展了在回归时间序列中定位变更点的方法，并为我们的变更点估计器建立急剧误差范围。进行了大量的数值实验和宏观经济学中的实际数据应用，以证明拟议的测试的有希望的性能和实用性。
In this paper, we study change-point testing for high-dimensional linear models, an important problem that has not been well explored in the literature. Specifically, we propose a quadratic-form cumulative sum (CUSUM) statistic to test the stability of regression coefficients in high-dimensional linear models. The test controls type-I error at any desired level and is robust to temporally dependent observations. We establish its asymptotic distribution under the null hypothesis, and demonstrate that it is asymptotically powerful against multiple change-point alternatives and achieves the optimal detection boundary for a wide class of high-dimensional models. We further develop an adaptive procedure to estimate the tuning parameters of the test, making our method practical in applications. Additionally, we extend our approach to localize change-points in the regression time series and establish sharp error bounds for our change-point estimator. Extensive numerical experiments and a real data application in macroeconomics are conducted to demonstrate the promising performance and practical utility of the proposed test.
