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Entropy
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Statistical Methods for Modeling High-Dimensional and Complex Data: Third Edition
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Statistical Methods for Modeling High-Dimensional and Complex Data: Third Edition

A special issue of Entropy (ISSN 1099-4300). This special issue belongs to the section "Information Theory, Probability and Statistics".

Deadline for manuscript submissions: 31 December 2026 | Viewed by 1584

Editor

Prof. Dr. Yuehua Wu

E-Mail Website
Guest Editor
Department of Mathematics and Statistics, York University, Toronto, ON M3J 1P3, Canada
Interests: statistical modeling and inference for data with a very complex structure and/or with high dimension
Special Issues, Collections and Topics in MDPI journals

Special Issue Information

Dear Colleagues,

Statistical models help us understand the structure of systems or processes in various fields, including engineering, the natural sciences, and the social sciences. One of the most important tasks in statistics is the development of methods and theories for building statistical models for datasets, which are approximations of the reality embodied in the observed data. In general, such models are not unique. For a given set of competing models, it is crucial to select the best approximation model among them before conducting statistical analysis.

Since data often exhibit complex structures, statistical models are expected to capture this complexity, which can further deepen our understanding of the underlying data-generating mechanisms and advance related fields in science and engineering. This Special Issue calls for newly developed statistical methods to model high-dimensional, complex data, especially methods based on entropy or information theory.

Prof. Dr. Yuehua Wu
Guest Editor

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. Entropy is an international peer-reviewed open access monthly 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

  • model selection
  • spatiotemporal modeling
  • cluster analysis
  • high-dimensional statistics
  • data mining
  • multiple change-point detection

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Related Special Issues

Published Papers (2 papers)

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Research

34 pages, 2605 KB  
Article
Quasi-Maximum Exponential Likelihood Estimation of Conditional Quantiles for GARCH Models Based on High-Frequency Augmented Data
by Zhenming Zhang, Shishun Zhao, Jianhua Cheng and Anze Wang
Entropy 2026, 28(3), 326; https://doi.org/10.3390/e28030326 - 13 Mar 2026
Viewed by 469
Abstract
GARCH models play a fundamental role in modeling time-varying volatility in financial return series. In practice, financial returns are also well known to exhibit heavy-tailed distributions, which naturally motivates the use of quasi-maximum exponential likelihood estimation (QMELE) for accurately capturing tail behavior and [...] Read more.
GARCH models play a fundamental role in modeling time-varying volatility in financial return series. In practice, financial returns are also well known to exhibit heavy-tailed distributions, which naturally motivates the use of quasi-maximum exponential likelihood estimation (QMELE) for accurately capturing tail behavior and risk measures such as Value-at-Risk. At the same time, the increasing availability of intraday high-frequency data has led to the development of high-frequency augmented GARCH models, which incorporate intraday information into conventional low-frequency volatility frameworks. By exploiting transaction-level data recorded at very fine time scales, these models are able to capture intraday volatility dynamics and market microstructure effects that are not reflected in standard low-frequency observations. Against this background, this paper studies conditional quantile estimation for high-frequency augmented GARCH models. We develop QMELE-based estimators for both model parameters and conditional quantiles, and construct an adjusted test statistic for assessing model adequacy. The asymptotic properties of the proposed estimators and test statistic are established, and their finite-sample performance is examined through extensive simulation studies. Empirical applications to three major stock indices demonstrate that augmenting GARCH models with high-frequency information leads to substantial improvements in conditional quantile estimation compared with traditional low-frequency approaches. Full article
(This article belongs to the Special Issue Statistical Methods for Modeling High-Dimensional and Complex Data: Third Edition)
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19 pages, 376 KB  
Article
Multi-Platform Multivariate Regression with Group Sparsity for High-Dimensional Data Integration
by Shanshan Qin, Guanlin Zhang, Xin Gao and Yuehua Wu
Entropy 2026, 28(2), 135; https://doi.org/10.3390/e28020135 - 23 Jan 2026
Viewed by 583
Abstract
High-dimensional regression with multivariate responses poses significant challenges when data are collected across multiple platforms, each with potentially correlated outcomes. In this paper, we introduce a multi-platform multivariate high-dimensional linear regression (MM-HLR) model for simultaneously modeling within-platform correlation and cross-platform information fusion. Our [...] Read more.
High-dimensional regression with multivariate responses poses significant challenges when data are collected across multiple platforms, each with potentially correlated outcomes. In this paper, we introduce a multi-platform multivariate high-dimensional linear regression (MM-HLR) model for simultaneously modeling within-platform correlation and cross-platform information fusion. Our approach incorporates a mixture of Lasso and group Lasso penalties to promote both individual predictor sparsity and cross-platform group sparsity, thereby enhancing interpretability and estimation stability. We develop an efficient computational algorithm based on iteratively reweighted least squares and block coordinate descent to solve the resulting regularized optimization problem. We establish theoretical guarantees for our estimator, including oracle bounds on prediction error, estimation accuracy, and support recovery under mild conditions. Our simulation studies confirm the method’s strong empirical performance, demonstrating low bias, small variance, and robustness across various dimensions. The analysis of real financial data further validates the performance gains achieved by incorporating multivariate responses and integrating data across multiple platforms. Full article
(This article belongs to the Special Issue Statistical Methods for Modeling High-Dimensional and Complex Data: Third Edition)
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