Statistical Inference and Analysis of High-Dimensional Data

A Special Issue of Mathematics (ISSN 2227-7390) belonging to the section "D: Statistics and Operational Research".

Deadline for manuscript submissions: 15 February 2027 | Viewed by 505

Editor


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Guest Editor
Guangdong Provincial/Zhuhai Key Laboratory of Interdisciplinary Research and Application for Data Science, Department of Statistics and Data Science, Beijing Normal-Hong Kong Baptist University, 2000 Jintong Road, Tang Jia Wan, Zhuhai 519087, China
Interests: minimum chi-square estimation; representative points; laplace distribution; dimension reduction; scrna-seq data

Special Issue Information

Dear Colleagues,

The exponential growth of modern datasets—featuring thousands of variables, complex dependencies, and often limited sample sizes—has fundamentally reshaped the landscape of statistical research. To address these challenges, we are pleased to announce a Special Issue of Mathematics dedicated to recent breakthroughs in the “Statistical Inference and Analysis of High-Dimensional Data”. This Special Issue aims to bridge theory and application, with a particular focus on three cutting-edge directions. We invite contributions advancing dimension reduction techniques in parametric and nonparametric statistical inference, including sparse modeling, sufficient dimension reduction, and penalized methods for complex dependency structures. We also seek works on linear and nonlinear dimension reduction for high-dimensional data visualization, from classical PCA to manifold learning, t-SNE, and UMAP, with an emphasis on interpretability and theoretical guarantees. Finally, we encourage submissions exploring high-dimensional techniques based on one-dimensional projection, such as projection pursuit, random projection, and the jackknife empirical likelihood for low-dimensional representations. Both methodological innovations and rigorous case studies are welcome. Join us to shape the future of inference in high dimensions.

Dr. Jiajuan Liang
Guest Editor

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Keywords

  • dimension reduction
  • parametric/nonparametric inference
  • high-dimensional visualization
  • projection pursuit
  • nonlinear manifolds
  • random projection

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Published Papers (1 paper)

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Research

16 pages, 322 KB  
Article
A Dimension-Reduction Method for Detecting Non-Multinormality in Two-Level Structural Equation Models
by Yiwen Cao, Jiajuan Liang and Chi-Kin Lam
Mathematics 2026, 14(16), 3020; https://doi.org/10.3390/math14163020 - 21 Aug 2026
Viewed by 278
Abstract
Testing multinormality in two-level structural equation models (SEMs) presents a fundamental challenge because observations from the same level-2 unit are correlated, violating the independence assumption required by classical normality tests. In this paper, we develop a novel generalized Shapiro–Wilk (GW) [...] Read more.
Testing multinormality in two-level structural equation models (SEMs) presents a fundamental challenge because observations from the same level-2 unit are correlated, violating the independence assumption required by classical normality tests. In this paper, we develop a novel generalized Shapiro–Wilk (GW) test that explicitly accounts for this dependence. The proposed method rearranges the dependent observations into a random matrix and employs principal component analysis (PCA) to project this matrix onto a set of principal directions, achieving effective dimension reduction. On each projected direction, the scale-invariant Shapiro–Wilk statistic is applied to test for sphericity, leveraging the property that spherical distributions preserve the null distribution of such statistics. The Johnson SB-transform is then used to approximate the null distribution of the combined test statistic. A Monte Carlo study demonstrates that the proposed GW test controls type I error rates satisfactorily and exhibits strong power against a range of non-normal alternatives, including heavy-tailed and asymmetric distributions. The method is further illustrated using real alcohol use data from nested families, highlighting its practical utility. Comparative evaluation indicates that the GW test performs favorably relative to a recently proposed approach. The procedure is applicable to balanced level-1 designs and provides researchers with a necessary diagnostic tool for assessing multinormality assumptions in two-level SEMs. Full article
(This article belongs to the Special Issue Statistical Inference and Analysis of High-Dimensional Data)
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