AI 中文总结
针对独立观测序列变点检测问题，提出LBD-FDR方法，可控制错误发现率，在高斯序列等场景下达最优检测性能，模拟中与五种现有方法对比验证有效性。
AI 中文摘要
我们研究在独立观测序列中检测和定位数量不断增长的变点的问题。我们提出了一种新方法Lean Bonferroni Detection - False Discovery Rate（LBD-FDR），该方法会在数据序列中生成一组定位区域，预期其中高比例的区域包含变点。LBD-FDR在广泛的分布场景中保证错误发现率的控制，包括具有挑战性的独立非参数和重尾数据场景。对于独立高斯序列，我们推导了变点排列的条件，在此条件下，该方法能一致地检测所有具有足够大信号的变点，同时不受无法检测的变点影响，并且我们证明LBD-FDR在某些场景下可获得最优检测常数。此外，我们推导了所提方法比极小极大最优I型错误控制方法更具功效的场景。最后，我们开发了LBD-FDR的计算可行算法，并在模拟中将其与五种现有方法进行比较。
英文摘要
We consider the problem of detecting and localizing a growing number of changepoints in a sequence of independent observations. We propose a new method, Lean Bonferroni Detection - False Discovery Rate (LBD-FDR), which produces a set of localized regions in the data sequence where, in expectation, a high proportion of them contain a changepoint. LBD-FDR guarantees control of the false discovery rate in a wide range of distributional settings, including the challenging case of independent non-parametric and heavy-tailed data. For independent Gaussian sequences, we derive conditions on changepoint arrangements where the method consistently detects all changepoints with a large enough signal while simultaneously being unaffected by those that are undetectable, and we show that LBD-FDR obtains the optimal detection constant in certain regimes. Moreover, we derive the settings where our method is more powerful than the minimax optimal Type I error controlling method. We finally develop a computationally feasible algorithm for the LBD-FDR and compare it in simulation to five existing procedures.
Comments46 pages, 3 figures
