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局部平稳过程的贝叶斯非参数谱分析AI 解读

Stationarity plays a pivotal role in time series analysis. It is not only the basis for the derivation of general asymptotic theory but it also allows an efficient analysis in the frequency domain via the Whittle likelihood, based on the asymptotic independence of the Fourier coefficients. However, many regularly sampled data derived from the observation of physical or ecological processes, for instance, are only locally stationary. They exhibit slowly evolving spectra and…

M 依赖随机场异常检测的扫描统计量及图像应用AI 解读

Anomaly detection in random fields is an important problem in many applications including the detection of cancerous cells in medicine, obstacles in autonomous driving and cracks in the construction material of buildings. Such anomalies are often visible as areas with different expected values compared to the background noise. Scan statistics based on local means have the potential to detect such local anomalies by enhancing relevant features. We derive limit theorems for a…

Page 之后七十年：累积和序贯变点检验的发展现状AI 解读

Abstract Quality control charts aim at raising an alarm as soon as sequentially obtained observations of an underlying random process no longer seem to be within stochastic fluctuations prescribed by an in-control scenario. Such random processes can often be modelled using the concept of stationarity, or even independence as in most classical works. An important out-of-control scenario is the changepoint alternative, for which the distribution of the process changes at an…

小波系数之间的依赖包含多少信息？AI 解读

This article is motivated by several articles that propose statistical inference where the independence of wavelet coefficients for both short- as well as long-range dependent time series is assumed. We focus on the sample variance and investigate the influence of the dependence between wavelet coefficients and this statistic. To this end, we derive asymptotic distributional properties of the sample variance for a time series that is synthesized, ignoring some or all…

多元时间序列变化检测及其脑电数据应用AI 解读

The primary contributions of this article are rigorously developed novel statistical methods for detecting change points in multivariate time series. We extend the class of score type change point statistics considered in 2007 by Hušková, Prášková, and Steinebach to the vector autoregressive (VAR) case and the epidemic change alternative. Our proposed procedures do not require the observed time series to actually follow the VAR model. Instead, following the strategy…

TFT自助法：频域重抽样与时域时间序列复制AI 解读

A new time series bootstrap scheme, the time frequency toggle (TFT)-bootstrap, is proposed. Its basic idea is to bootstrap the Fourier coefficients of the observed time series, and then to back-transform them to obtain a bootstrap sample in the time domain. Related previous proposals, such as the “surrogate data” approach, resampled only the phase of the Fourier coefficients and thus had only limited validity. By contrast, we show that the appropriate resampling of phase and…