Frequency Detection and Change Point Estimation for Time Series of Complex Oscillation
复杂振荡时间序列的频率检测与变点估计AI 解读 ↓
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AI 根据所提供的论文材料归类：摘要明确研究非平稳时间序列的频率检测与变点定位，方法对应时间序列及结构变化，应用对象为生理信号。
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复杂振荡时间序列的频率检测与变点估计
- 研究问题
- 当信号被数据生成机制复杂变化的非平稳噪声污染时，如何检测其振荡频率，并定位振荡模式发生变化的时间点？
- 方法与思路
- 作者先用高维密集渐进周期图检验检测频率，再以相位调整的局部算法定位变点，并建立高斯近似与重叠块乘子自助法。
- 材料陈述的贡献
- 摘要称，方法可渐近以预设概率在精确范围内检测频率及变点，并为无方差下界的复值高维非平稳序列建立相关推断工具。
- 阅读关注点
- 应核对噪声非平稳性、频率间隔和信号强度的允许范围，检测与定位误差的具体表述，以及自助法校准和相位调整的作用。
- 阅读边界
- 仅据 OpenAlex 索引摘要，稿件版本未注明；精度范围和成立条件未展开，应用为睡眠脑电，不能据此推断宏观数据上的同等表现。
原文摘要
We consider detecting the evolutionary oscillatory pattern of a signal when it is contaminated by nonstationary noises with complexly time-varying data generating mechanism. A high-dimensional dense progressive periodogram test is proposed to accurately detect all oscillatory frequencies. A further phase-adjusted local change point detection algorithm is applied in the frequency domain to detect the locations at which the oscillatory pattern changes. Our method is shown to be able to detect all oscillatory frequencies and the corresponding change points within an accurate range with a prescribed probability asymptotically. A Gaussian approximation scheme and an overlapping-block multiplier bootstrap methodology for sums of complex-valued high dimensional nonstationary time series without variance lower bounds are established, which could be of independent interest. This study is motivated by oscillatory frequency estimation and change point detection problems encountered in physiological time series analysis. An application to spindle detection and estimation in electroencephalogram recorded during sleep is used to illustrate the usefulness of the proposed methodology. Supplementary materials for this article are available online including a standardized description of the materials available for reproducing the work.