论文标题
复杂振荡时间序列的频率检测和变化点估计
Frequency Detection and Change Point Estimation for Time Series of Complex Oscillation
论文作者
论文摘要
当信号被非平稳的噪声污染时，我们考虑检测信号的进化振荡模式，并具有复杂的时间变化的数据生成机制。提出了高维密度的渐进期遗期测试，以准确检测所有振荡频率。在频域中应用了进一步的相调整的局部变化点检测算法，以检测振荡模式变化的位置。我们的方法显示能够检测所有振荡频率和准确范围内的相应变更点，并渐近规定的概率。这项研究是由生理时间序列分析中遇到的振荡频率估计和变化点检测问题的动机。用于主轴检测和估计睡眠脑电图数据的应用用于说明所提出的方法的有用性。为了建立了没有方差下限的复杂评估高维非平稳时间序列的总和，一种高斯近似方案和重叠块乘数引导方法，可引起独立的利益。
We consider detecting the evolutionary oscillatory pattern of a signal when it is contaminated by non-stationary 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. 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 sleep EEG data is used to illustrate the usefulness of the proposed methodology. A Gaussian approximation scheme and an overlapping-block multiplier bootstrap methodology for sums of complex-valued high dimensional non-stationary time series without variance lower bounds are established, which could be of independent interest.
