具有时间相关噪声的大规模数据的半参数推理

IF 1 4区 数学 Q3 STATISTICS & PROBABILITY Electronic Journal of Statistics Pub Date : 2023-01-01 DOI:10.1214/23-ejs2171
Chunming Zhang, Xiao Guo, Min Chen, Xinze Du
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引用次数: 0

摘要

在神经科学和气象学等领域的科学研究中,时间依赖性经常出现在大规模结构化噪声数据中。这个具有挑战性的特征可能与现有的理论框架或数据分析工具不一致。受多时段fMRI时间序列数据的启发,本文介绍了一种新的半参数推理方法,适用于时间过程数据中广泛的“非平稳、非高斯、时间相关”噪声过程。提出了一种基于大维噪声自协方差矩阵的锥型估计量的检验统计量,并建立了其渐近卡方分布。该方法不仅放宽了对噪声协方差矩阵估计的一致性要求,而且在不牺牲检测能力的情况下避免了矩阵的直接反演。它可以很好地适应平稳和更大范围的时间噪声过程,使其特别有效地处理涉及非常大数据规模和大尺寸噪声协方差矩阵的具有挑战性的场景。我们通过模拟评估和真实fMRI数据分析证明了所提出程序的有效性。
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Semi-parametric inference for large-scale data with temporally dependent noise
Temporal dependence is frequently encountered in large-scale structured noisy data, arising from scientific studies in neuroscience and meteorology, among others. This challenging characteristic may not align with existing theoretical frameworks or data analysis tools. Motivated by multi-session fMRI time series data, this paper introduces a novel semi-parametric inference procedure suitable for a broad class of “non-stationary, non-Gaussian, temporally dependent” noise processes in time-course data. It develops a new test statistic based on a tapering-type estimator of the large-dimensional noise auto-covariance matrix and establishes its asymptotic chi-squared distribution. Our method not only relaxes the consistency requirement for the noise covariance matrix estimator but also avoids direct matrix inversion without sacrificing detection power. It adapts well to both stationary and a wider range of temporal noise processes, making it particularly effective for handling challenging scenarios involving very large scales of data and large dimensions of noise covariance matrices. We demonstrate the efficacy of the proposed procedure through simulation evaluations and real fMRI data analysis.
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来源期刊
Electronic Journal of Statistics
Electronic Journal of Statistics STATISTICS & PROBABILITY-
CiteScore
1.80
自引率
9.10%
发文量
100
审稿时长
3 months
期刊介绍: The Electronic Journal of Statistics (EJS) publishes research articles and short notes on theoretical, computational and applied statistics. The journal is open access. Articles are refereed and are held to the same standard as articles in other IMS journals. Articles become publicly available shortly after they are accepted.
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