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Mathematics
Special Issues
New Challenges in Statistical Analysis and Multivariate Data Analysis
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New Challenges in Statistical Analysis and Multivariate Data Analysis

A special issue of Mathematics (ISSN 2227-7390). This special issue belongs to the section "D1: Probability and Statistics".

Deadline for manuscript submissions: 20 March 2027 | Viewed by 1490

Editors

Dr. Sungsu Kim

E-Mail Website
Guest Editor
Resch School of Engineering, University of Wisconsin-Green Bay, Green Bay, WI, USA
Interests: circular statistics; multivariate analysis; bioinformatics; stochastic process
Special Issues, Collections and Topics in MDPI journals
Dr. Chi Seng Pun

E-Mail Website
Guest Editor
School of Physical & Mathematical Sciences, Nanyang Technological University, Singapore 637371, Singapore
Interests: applied mathematics and statistics; mathematical finance; risk management; stochastic analysis

Special Issue Information

Dear Colleagues,

This Special Issue welcomes high-quality original research and review articles focused on recent developments and ongoing challenges in statistical and multivariate data analysis. We encourage submissions that present novel methodologies, cutting-edge computational techniques, and interdisciplinary applications across fields such as environmental science, public health, economics, and the social sciences.

Topics of interest include high-dimensional data analysis, robust and nonparametric methods, machine learning integration, and advanced multivariate modeling techniques.

The goal of this Issue is to provide a platform for researchers and practitioners to share innovative ideas, promote cross-disciplinary collaboration, and contribute to the advancement of modern data analysis.

Dr. Sungsu Kim
Dr. Chi Seng Pun
Guest Editors

Manuscript Submission Information

Manuscripts should be submitted online at www.mdpi.com by registering and logging in to this website. Once you are registered, click here to go to the submission form. Manuscripts can be submitted until the deadline. All submissions that pass pre-check are peer-reviewed. Accepted papers will be published continuously in the journal (as soon as accepted) and will be listed together on the special issue website. Research articles, review articles as well as short communications are invited. For planned papers, a title and short abstract (about 250 words) can be sent to the Editorial Office for assessment.

Submitted manuscripts should not have been published previously, nor be under consideration for publication elsewhere (except conference proceedings papers). All manuscripts are thoroughly refereed through a single-anonymized peer-review process. A guide for authors and other relevant information for submission of manuscripts is available on the Instructions for Authors page. Mathematics is an international peer-reviewed open access semimonthly journal published by MDPI.

Please visit the Instructions for Authors page before submitting a manuscript. The Article Processing Charge (APC) for publication in this open access journal is 2600 CHF (Swiss Francs). Submitted papers should be well formatted and use good English. Authors may use MDPI's English editing service prior to publication or during author revisions.

Keywords

  • machine learning
  • high-dimensional statistics
  • functional data analysis
  • sparse learning

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Further information on MDPI's Special Issue policies can be found here.

Published Papers (3 papers)

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Research

36 pages, 35340 KB  
Article
A Fault Diagnosis Method Based on MCAG-ResNet for Industrial Processes
by Feng Yu, Hong Yuan and Jihan Li
Mathematics 2026, 14(13), 2363; https://doi.org/10.3390/math14132363 - 2 Jul 2026
Viewed by 186
Abstract
Industrial process fault diagnosis remains challenging because one-dimensional time-series data often involve complex dynamics, noise disturbances, and temporal dependencies, which hinder reliable fault representation and robust diagnostic decisions under complex operating conditions. To address these challenges, a fault diagnosis method for industrial processes [...] Read more.
Industrial process fault diagnosis remains challenging because one-dimensional time-series data often involve complex dynamics, noise disturbances, and temporal dependencies, which hinder reliable fault representation and robust diagnostic decisions under complex operating conditions. To address these challenges, a fault diagnosis method for industrial processes based on the Multiscale Convolution-Attention-GRU Residual Network (MCAG-ResNet) is proposed. MCAG-ResNet integrates multiscale feature learning, attention-based feature recalibration, temporal dependency modeling, and residual learning in a unified architecture to enhance discriminative fault representation and diagnostic robustness. In addition, normalization and lightweight data augmentation are incorporated to improve training stability and generalization performance. Validation on the Tennessee Eastman (TE) and Continuous Stirred Tank Reactor (CSTR) datasets demonstrates the effectiveness, generalization capability, and diagnostic stability of the MCAG-ResNet in complex industrial process fault diagnosis. Further analyses, including variable contribution, feature importance, noise robustness, hyperparameter sensitivity, performance–complexity, and statistical stability analyses, verify its interpretability, robustness, parameter rationality, practical applicability, and stability. Full article
(This article belongs to the Special Issue New Challenges in Statistical Analysis and Multivariate Data Analysis)
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17 pages, 2960 KB  
Article
An Enhanced Multivariate EWMA Approach with Variable Selection and Adaptive Sampling for Efficient Process Monitoring
by Anan Tang, Juncheng Xu and Yuanman Ma
Mathematics 2026, 14(10), 1670; https://doi.org/10.3390/math14101670 - 14 May 2026
Viewed by 352
Abstract
Due to the curse of dimensionality faced in modern industrial processes, high-dimensional Statistical Process Control (SPC) faces significant challenges in detecting small and sparse process shifts. Traditional multivariate control charts often suffer from noise accumulation and fail at timely identification of anomalies that [...] Read more.
Due to the curse of dimensionality faced in modern industrial processes, high-dimensional Statistical Process Control (SPC) faces significant challenges in detecting small and sparse process shifts. Traditional multivariate control charts often suffer from noise accumulation and fail at timely identification of anomalies that affect only a small subset of variables. To address this issue, this study proposes an enhanced Multivariate Exponentially Weighted Moving Average (MEWMA) approach with variable selection and adaptive sampling for efficient process monitoring. The proposed smart approach works in two ways: first, it automatically focuses on the variables that are most likely to have changed (variable selection); second, it takes samples more frequently when things look uncertain, and less frequently when everything appears stable (variable sampling interval). This combination allows problems to be detected earlier. A Monte Carlo approach is used to calculate the the Average Time to Signal (ATS) values of the proposed scheme, and comparative results show that the proposed scheme outperforms standard charts like the Fixed Sampling Intervals (FSI) VSME, VSI-T2, and VSI-MEWMA schemes in terms of detection speed for small-to-moderate sparse shifts. Finally, a real example from car body manufacturing is provided as an illustration for the implementation of the proposed scheme. Full article
(This article belongs to the Special Issue New Challenges in Statistical Analysis and Multivariate Data Analysis)
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39 pages, 507 KB  
Article
An LM-Type Unit Root Test for Functional Time Series
by Yichao Chen and Chi Seng Pun
Mathematics 2026, 14(5), 916; https://doi.org/10.3390/math14050916 - 8 Mar 2026
Cited by 1 | Viewed by 450
Abstract
In this paper, we propose a Lagrange multiplier (LM)-type unit root test for functional time series. The key novelty lies not in introducing a new LM principle but in establishing the asymptotic validity of such a test under the functional random walk null [...] Read more.
In this paper, we propose a Lagrange multiplier (LM)-type unit root test for functional time series. The key novelty lies not in introducing a new LM principle but in establishing the asymptotic validity of such a test under the functional random walk null hypothesis without relying on functional principal component analysis (FPCA) or finite-dimensional unit root subspace assumptions. We derive the limit distribution of our proposed test statistics under the null hypothesis of a random walk and its asymptotic behavior of alternative hypotheses of trend stationary, weakly dependent stationary, and autoregressive stationary models. Specifically, we establish the theoretical consistency of the test under all aforementioned alternative hypotheses. Simulation studies corroborate these theoretical findings and demonstrate the desirable finite-sample performance of the proposed functional unit root test. The proposed test is also applied to real data of intraday stock price curves, and the test results are plausible. Full article
(This article belongs to the Special Issue New Challenges in Statistical Analysis and Multivariate Data Analysis)
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