Open Access
2023 Semi-parametric inference for large-scale data with temporally dependent noise
Chunming Zhang, Xiao Guo, Min Chen, Xinze Du
Author Affiliations +
Electron. J. Statist. 17(2): 2962-3007 (2023). DOI: 10.1214/23-EJS2171


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.

Funding Statement

C. Zhang’s work was supported by U.S. National Science Foundation grants DMS-2013486 and DMS-1712418, and provided by the University of Wisconsin-Madison Office of the Vice Chancellor for Research and Graduate Education with funding from the Wisconsin Alumni Research Foundation. M. Chen’s research was supported by the National Natural Science Foundation of China, grants 11690014 and 11731051. X. Guo’s research is supported by the National Natural Science Foundation of China, grant 12071452.


The authors thank the Editor, Associate Editor, and three reviewers for their insightful comments.


Download Citation

Chunming Zhang. Xiao Guo. Min Chen. Xinze Du. "Semi-parametric inference for large-scale data with temporally dependent noise." Electron. J. Statist. 17 (2) 2962 - 3007, 2023.


Received: 1 August 2022; Published: 2023
First available in Project Euclid: 10 November 2023

Digital Object Identifier: 10.1214/23-EJS2171

Primary: 62F35
Secondary: 62F12 , 62F30

Keywords: Auto-covariance matrix , False discovery rate , fMRI , neuroimaging , partially-linear model

Vol.17 • No. 2 • 2023
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