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Statistical Analysis and Data Science for Complex Data, 2nd Edition

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A Special Issue of Mathematics (ISSN 2227-7390) belonging to the section "D1: Probability and Statistics".

Deadline for manuscript submissions: 31 December 2026 | Viewed by 4474

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Dr. Li-pang Chen

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Department of Statistics, National Chengchi University, Taipei 116, Taiwan
Interests: graphical models; high-dimensional data analysis; machine learning; measurement error and error classification; survival analysis
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Dear Colleagues,

Nowadays, thanks to the rapid development of technology, datasets can be collected easily in many fields, such as biology, manufacturing, etc. Typically, given a dataset, one may encounter situations wherein (i) the sample size is large or (ii) the dimension of variables is large, yielding so-called big data or high-dimensional data, respectively. However, rare samples or variables are informative in data analysis. On the other hand, datasets usually contain complex structures caused by the collection procedure, such as censoring, measurement errors, or missingness. With noisy data, it becomes more challenging to choose informative subdata, detect important variables, or conduct analyses. In light of these challenges, this Special Issue will provide a platform for publishing novel statistical methods and algorithms that handle these complex structures in various research fields. Topics of interest for this Special Issue include biostatistics, bioinformatics, causal inference, statistical process control, and survival analysis.

Dr. Li-pang Chen
Guest Editor

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Keywords

algorithm
big data
high dimensionality
noisy data

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Published Papers (6 papers)

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Research

37 pages, 680 KB

Open AccessArticle

Laplace Factor Models in High-Dimensional Data

by Siqi Liu, Xuerong Meggie Wen, Akim Adekpedjou and Guangbao Guo

Mathematics 2026, 14(15), 2853; https://doi.org/10.3390/math14152853 - 6 Aug 2026

Viewed by 295

Abstract

Laplace factor models (LFMs) provide a heavy-tailed alternative to Gaussian factor models by representing high-dimensional observations through a low-rank common component and Laplace-distributed idiosyncratic errors. This paper develops an assumption-consistent finite-sample analysis of matrix concentration, covariance estimation, and Monte Carlo integration under this model. We first formulate the model with explicit dimensional, independence, covariance, and identifiability conditions. Standard matrix Laplace-transform and matrix Bernstein inequalities are then recalled with their precise applicability conditions. Because untruncated Laplace variables are neither almost surely bounded nor strongly log-concave, these standard results cannot be applied directly in the forms commonly used for bounded or Gaussian-like observations. To address this issue, we analyze a coordinatewise truncated covariance estimator and derive an operator-norm bound that separates the stochastic estimation error from the truncation bias. The resulting rate depends on the effective rank and the logarithm of the ambient dimension and is therefore not dimension-free. For Monte Carlo integration, we replace strong-log-concavity arguments by a sub-exponential concentration analysis that is compatible with independent Laplace errors and yields non-asymptotic absolute- and relative-error bounds. Simulation studies compare empirical tails with the classical matrix Bernstein bound, evaluate ordinary, truncated, winsorized, PCA, POET-type, and Huberized covariance estimators, and we compare Laplace-based and Studentized confidence intervals. The results show that the classical Bernstein bound can be conservative, and truncation involves a substantial bias–variance trade-off. In a Wine chemical-analysis application, three factors explain 66.53% of the standardized variance, and POET-type covariance estimation attains a cross-validated balanced accuracy of 0.9901. These findings clarify both the scope and the limitations of finite-sample analysis for LFMs. Full article

(This article belongs to the Special Issue Statistical Analysis and Data Science for Complex Data, 2nd Edition)

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23 pages, 3138 KB

Open AccessArticle

Research on the Spillover Effects Among Artificial Intelligence, New Energy Industry, and High-Carbon-Emission Industries from a Time–Frequency Perspective

by Ruijie Song, Xuebing Li, Mengzao Wang and Soonhu Soh

Mathematics 2026, 14(13), 2449; https://doi.org/10.3390/math14132449 - 7 Jul 2026

Viewed by 489

Abstract

Artificial intelligence (AI) technology has become the core force driving industrial transformation in today’s world. In-depth exploration of the spillover effects between artificial intelligence and new energy, as well as high-carbon-emission industries is of great significance for optimizing the industrial structure, preventing systemic risks in the industrial system, and achieving high-quality development. Based on the DY and BK spillover index model under the TVP-VAR framework, this paper analyzes the spillover effects between artificial intelligence and new energy, as well as high-carbon-emission industries from a time–frequency perspective, and constructs a spillover network to analyze the risk spillover transmission path. Finally, it explores the optimal investment portfolio weights and investment hedging strategies in the financial market. The results show that there is a significant static spillover effect between artificial intelligence and new energy, as well as high-carbon-emission industries. The intensity of this effect follows the pattern of “short-term > medium-term > long-term”. Moreover, new energy and some high-carbon-emission industries (such as the non-ferrous metals industry, the petrochemical industry, and the chemical industry) are the net spillover sources, while artificial intelligence and some high-carbon-emission industries (such as the power industry, the building materials industry, and the aerospace industry) are the net receiving parties. The dynamic spillover effect exhibits significant time-varying characteristics, being significantly impacted by major events such as environmental protection policies, the COVID-19 pandemic, and technological innovations. The chemical industry is the largest spillover outputter in all frequency domains, while the building materials industry is the largest receiver. From the perspective of the spillover network, the artificial intelligence industry, as a key node of the spillover network, plays a crucial role in the transmission of risk spillover. From the perspective of investment practice, the minimum connectedness portfolio (MCoP) performs well in terms of risk hedging effectiveness and return performance and may be the best choice for investors to balance risk and return. Full article

(This article belongs to the Special Issue Statistical Analysis and Data Science for Complex Data, 2nd Edition)

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14 pages, 7420 KB

Open AccessArticle

Research on Spare Part Activation Strategy and Reliability Index Calculation of Cold Standby Voting Systems Under Weibull Distribution

by Ziwen Yang, Xiaochuan Ai, Longlong Liu and Jun Wu

Mathematics 2026, 14(9), 1533; https://doi.org/10.3390/math14091533 - 30 Apr 2026

Viewed by 409

Abstract

This study investigates the impact of standby activation strategies on system reliability. The results show that a delayed activation strategy effectively improves system reliability. Additionally, to tackle the difficulty of deriving analytical solutions for reliability metrics under the Weibull distribution, a non-homogeneous Markov model based on the delayed activation strategy is introduced. The system’s residual life is modeled computationally using the state transition method. The numerical results suggest that the proposed method aligns closely with Monte Carlo simulations. It significantly improves computational efficiency while maintaining high accuracy, thus confirming its effectiveness. Full article

(This article belongs to the Special Issue Statistical Analysis and Data Science for Complex Data, 2nd Edition)

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22 pages, 4293 KB

Open AccessArticle

Modeling Comovement and Asynchrony Between Fossil and Clean Energy Markets Under Climate Risks Using Quantile-on-Quantile Connectedness

by Mengyue Liu, Rufei Zhang, Yuanyuan Jiang and Wang Gao

Mathematics 2026, 14(9), 1486; https://doi.org/10.3390/math14091486 - 28 Apr 2026

Viewed by 576

Abstract

This paper examines how climate risk shapes the connectedness between fossil and clean energy markets. To do so, we use the quantile-on-quantile connectedness framework and extend it to the frequency domain to capture return and volatility spillovers across different market conditions and horizons. We further employ an autoregressive distributed lag (ARDL) model to assess the effects of physical and transition climate risks on the estimated connectedness structure. The results show that fossil and clean energy markets exhibit both comovement and asynchrony, although comovement is dominant overall. After decomposing connectedness into short-term and long-term components, we find that return spillovers are mainly driven by short-term dynamics, whereas volatility spillovers are mainly driven by long-term dynamics. In addition, climate risks significantly affect the connectedness structure between the two markets, and policy-related risk and global warming risk are particularly important in strengthening asynchronous features. These findings suggest that climate risk influences not only the strength of spillovers, but also the way fossil and clean energy markets interact under different market states. Full article

(This article belongs to the Special Issue Statistical Analysis and Data Science for Complex Data, 2nd Edition)

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30 pages, 3285 KB

Open AccessArticle

Causal Identification of Artificial Intelligence Effects on Enterprise Labor Structure via a Partially Linear Double Machine Learning Estimator: Evidence from High-Dimensional Panel Data

by Huali Liu, Wenjie Li, Yankai Lin and Zne-Jung Lee

Mathematics 2026, 14(8), 1312; https://doi.org/10.3390/math14081312 - 14 Apr 2026

Viewed by 927

Abstract

This study develops a semiparametric causal inference framework to quantify the effect of Artificial Intelligence (AI) adoption on enterprise labor structure under high-dimensional confounding. We employ the Double Machine Learning (DML) estimator proposed, which combines Neyman orthogonality and cross-fitting to achieve reliable causal identification in settings where conventional regression methods are prone to bias from high-dimensional controls and nonlinear confounding. Nuisance functions are estimated using Lasso and Random Forests, enabling flexible modeling of complex relationships between control variables and outcomes. Using an unbalanced panel of Chinese A-share listed companies spanning 2006 to 2023, we identify a significant positive average treatment effect of AI adoption on the share of high-skilled labor (estimate: 0.118; 95% CI: [0.073, 0.163]), indicating that complementarity between AI and skilled workers dominates substitution at the firm level. Heterogeneity analysis reveals that the effect is stronger in manufacturing (0.183) than in services (0.071), and more pronounced in Eastern China (0.142) than in Central and Western regions (0.079). Quantile regression further shows that the complementarity effect intensifies at higher skill quantiles. A Panel Smooth Transition Regression (PSTR) model identifies a digitalization threshold beyond which AI–skill complementarity further strengthens. Mediation analysis confirms that productivity enhancement, digital transformation, and innovation activities together account for the majority of the total effect, with productivity improvement alone contributing approximately 34%. Placebo tests and propensity score weighting validate the robustness of our findings. Full article

(This article belongs to the Special Issue Statistical Analysis and Data Science for Complex Data, 2nd Edition)

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36 pages, 2186 KB

Open AccessArticle

On a Beta-Gamma Discrete Distribution for Thunderstorm Count Modeling with Risk Analysis

by Tassaddaq Hussain, Enrique Villamor, Mohammad Shakil, Mohammad Ahsanullah and B. M. Golam Kibria

Mathematics 2025, 13(24), 3913; https://doi.org/10.3390/math13243913 - 7 Dec 2025

Cited by 1 | Viewed by 908

Abstract

Risk management is vital for financial institutions to evaluate and mitigate potential losses. Thunderstorm count modeling with risk analysis is used by various sectors, such as insurance and utility companies, to forecast storm recurrence, analyze risk, and estimate financial losses based on factors like wind speed, hail size, and tornado potential. This paper introduces a novel discrete distribution, the Beta-Gamma Discrete (BGD) distribution, designed for modeling count data that inherently excludes zero values. Developed through the compounding of a discrete gamma distribution with a beta distribution, the BGD offers significant flexibility in handling overdispersion and complex data characteristics. The study derives key statistical properties of the BGD, including its probability mass function, moments, hazard rate function, moment generating function, and mean residual life. A comprehensive characterization theorem is also established. The model’s practical utility is demonstrated through an application to thunderstorm event data from the Kennedy Space Center (KSC), where the frequency of thunderstorms per event is a critical operational concern. The performance of the BGD is thoroughly assessed against established zero-truncated models—namely, the Zero-Truncated Generalized Poisson (ZTGP), Size-Biased Negative Binomial (SBNB), and Zero-Truncated Generalized Negative Binomial (ZTGNB)—using evaluation criteria such as Akaike Information Criterion (AIC), Bayesian Information Criterion (BIC), Chi-square goodness-of-fit, and the Vuong test. The results consistently show that the BGD provides a superior and more accurate fit for the thunderstorm data, thus help NASA and other space agencies for establishing it as a robust and effective tool for modeling positive count data in meteorological and other applied contexts with risk analysis. Full article

(This article belongs to the Special Issue Statistical Analysis and Data Science for Complex Data, 2nd Edition)

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