Axioms

Research

41 pages, 700 KB

Open AccessArticle

The Distribution and Quantiles of Sample Autocovariances and Autocorrelations of Sample Moments from a Stationary Process

by Christopher Stroude Withers

Axioms 2026, 15(4), 281; https://doi.org/10.3390/axioms15040281 - 12 Apr 2026

Viewed by 296

Abstract

This paper gives expansions for the distribution, density and quantiles of any estimate that is a smooth function of the sample cross-moments of a stationary process. Three versions of these are given, depending on whether an exact, approximate, or asymptotic form is used [...] Read more.

This paper gives expansions for the distribution, density and quantiles of any estimate that is a smooth function of the sample cross-moments of a stationary process. Three versions of these are given, depending on whether an exact, approximate, or asymptotic form is used for the variance or covariance of the estimate. Eight examples are provided, including sample autocovariances and autocorrelations. Their Central Limit Theorems extend those in the literature, such as Bartlett’s formula, by allowing for the effect of the mean and higher order cross-cumulants. Their distribution and quantiles are given to magnitude

n^{- r / 2}

up to r = 3, where n is the sample size. Full article

(This article belongs to the Special Issue New Perspectives in Mathematical Statistics, 2nd Edition)

► Show Figures

Figure 1

18 pages, 331 KB

Open AccessArticle

Some Distributional Properties of the Matrix-Variate Generalized Gamma Model

by Arak M. Mathai and Serge B. Provost

Axioms 2026, 15(3), 238; https://doi.org/10.3390/axioms15030238 - 23 Mar 2026

Viewed by 556

Abstract

This paper employs Jacobians of matrix transformations to derive the density function of a matrix-variate generalized gamma distribution, together with its normalizing constant. By applying the inverse Mellin transform, explicit expressions for the density functions of the determinant and the trace are obtained [...] Read more.

This paper employs Jacobians of matrix transformations to derive the density function of a matrix-variate generalized gamma distribution, together with its normalizing constant. By applying the inverse Mellin transform, explicit expressions for the density functions of the determinant and the trace are obtained in terms of generalized hypergeometric functions. The characteristic function and the first two moments follow from an associated density generator. Both the real and complex cases are treated, and several important special cases are identified. A simulation study reveals that the proposed model provides a more accurate fit than other distributions that are also defined on the cone of positive definite matrices. Moreover, it is shown to exhibit superior performance when applied to two empirical data sets. Applications involving the modeling of scatter matrices arising in financial studies, biostatistics, and reliability analysis are also discussed. Full article

(This article belongs to the Special Issue New Perspectives in Mathematical Statistics, 2nd Edition)

36 pages, 4478 KB

Open AccessArticle

CBAM-BiLSTM-DDQN: A Novel Adaptive Quantitative Trading Model for Financial Data Analysis

by Yan Zhang, Mingxuan Zhou, Feng Sun and Yuehua Wu

Axioms 2026, 15(3), 222; https://doi.org/10.3390/axioms15030222 - 16 Mar 2026

Viewed by 967

Abstract

Financial data analysis remains a significant challenge due to the inherent stochasticity, non-stationarity, and low signal-to-noise ratio of market data. Conventional methods often struggle to disentangle intrinsic trends from noise and frequently overlook the critical influence of investor sentiment on price dynamics. To [...] Read more.

Financial data analysis remains a significant challenge due to the inherent stochasticity, non-stationarity, and low signal-to-noise ratio of market data. Conventional methods often struggle to disentangle intrinsic trends from noise and frequently overlook the critical influence of investor sentiment on price dynamics. To address these issues, we propose an adaptive trading model named CBAM-BiLSTM-DDQN, which integrates signal decomposition, multi-source feature fusion, and deep reinforcement learning. First, we construct a comprehensive heterogeneous feature set by combining price signals decomposed via Variational Mode Decomposition (VMD) and investor sentiment indices extracted from financial texts. Subsequently, a Genetic Algorithm (GA) is employed to identify the most significant feature subset, effectively reducing dimensionality and redundancy. Finally, these optimized features are input into a Double Deep Q-Network (DDQN) agent equipped with a Convolutional Block Attention Module (CBAM) and a Bidirectional Long Short-Term Memory (BiLSTM) network to capture complex spatiotemporal dependencies. We evaluated this approach through simulated trading on three major Chinese stock indices—the Shanghai Stock Exchange Composite (SSEC), the Shenzhen Stock Exchange Component (SZSE), and the China Securities 300 (CSI 300). Experimental results demonstrate the superiority of our method over traditional strategies and standard baselines; specifically, the trading agent achieved robust cumulative returns across the SSEC and CSI 300 indices, confirming the model’s exceptional capability in balancing profitability and risk aversion in complex financial environments. Furthermore, additional experiments on individual stocks in the Chinese A-share market reinforce the robustness and generalization ability of our proposed model, validating its practical potential for diverse trading scenarios. Furthermore, additional experiments on individual stocks in the Chinese A-share market reinforce the robustness and generalization ability of our proposed model, validating its practical potential for diverse trading scenarios. Full article

(This article belongs to the Special Issue New Perspectives in Mathematical Statistics, 2nd Edition)

► Show Figures

Figure 1

30 pages, 1036 KB

Open AccessArticle

Classical and Bayesian Inference for the Two-Parameter Chen Distribution with Random Censored Data

by Zihan Zhao, Wenhao Gui, Minghui Liu and Lanxi Zhang

Axioms 2026, 15(3), 213; https://doi.org/10.3390/axioms15030213 - 12 Mar 2026

Viewed by 441

Abstract

This study explores classical and Bayesian estimation for the two-parameter Chen distribution with randomly censored data, where censoring times follow an independent two-parameter Chen distribution with separate shape and scale parameters. We first derive the maximum likelihood estimators of the unknown parameters, together [...] Read more.

This study explores classical and Bayesian estimation for the two-parameter Chen distribution with randomly censored data, where censoring times follow an independent two-parameter Chen distribution with separate shape and scale parameters. We first derive the maximum likelihood estimators of the unknown parameters, together with their asymptotic variances and credible intervals, and further adopt the method of moments, L-moments and least squares methods for classical estimation. Under the generalized entropy loss function and inverse gamma priors, Bayesian estimation is implemented via Gibbs sampling, with the highest posterior density credible intervals of parameters constructed accordingly. We also investigate the estimation of key reliability and lifetime characteristics of the distribution, and conduct Monte Carlo simulations to compare the performance of all aforementioned estimation methods. Finally, two real-world CMAPSS jet engine lifetime datasets from NASA are applied to validate the practical effectiveness of the proposed estimation approaches, demonstrating the enhanced flexibility of the Chen distribution compared to the exponential distribution in fitting aerospace-related censored data, given the marginal p-values in the K-S tests. Full article

(This article belongs to the Special Issue New Perspectives in Mathematical Statistics, 2nd Edition)

► Show Figures

Figure 1

15 pages, 332 KB

Open AccessArticle

Testing Homogeneity of Odds Ratio for Stratified Bilateral Correlated Data

by Xi Shen, Xueqing Zhang and Chang-Xing Ma

Axioms 2026, 15(2), 155; https://doi.org/10.3390/axioms15020155 - 20 Feb 2026

Viewed by 355

Abstract

In clinical studies such as ophthalmologic or otolaryngologic research, bilateral correlated data frequently arise when outcomes are collected from paired organs or body parts. Since the measurements from such paired observations are usually highly correlated, appropriate data analysis requires accounting for the intra-class [...] Read more.

In clinical studies such as ophthalmologic or otolaryngologic research, bilateral correlated data frequently arise when outcomes are collected from paired organs or body parts. Since the measurements from such paired observations are usually highly correlated, appropriate data analysis requires accounting for the intra-class correlation. Methodological developments for analyzing bilateral data have been extensively studied over the past several decades, including both inferential procedures and computational strategies. In some analyses, the center effect or confounding effect could lead to imbalance among treatment arms, making it necessary to adjust for stratification/confounding factors in the data analysis. In this article, we develop three testing procedures for assessing the homogeneity of odds ratios in stratified bilateral correlated data under the assumption of a common correlation structure. Monte Carlo simulation studies are conducted to evaluate the performance of the proposed methods. The results indicate that the Wald-type test based on a log-linear hypothesis and the score test maintain robust type I error rates and achieve high power across a range of scenarios, and are therefore recommended for practical application. The proposed methodologies are further illustrated using two real data examples. Full article

(This article belongs to the Special Issue New Perspectives in Mathematical Statistics, 2nd Edition)

► Show Figures

Figure 1

21 pages, 903 KB

Open AccessArticle

A Discrete Analogue of the Exponentiated Generalized Weibull-G Family: A New Discrete Distribution with Different Methods of Estimation and Application

by Dawlah Alsulami

Axioms 2026, 15(2), 140; https://doi.org/10.3390/axioms15020140 - 14 Feb 2026

Viewed by 575

Abstract

Statistical distributions play a crucial role in analyzing real data with varying behavior. In this study, the exponentiated generalized Weibull-G family is discretized using the survival discretization method. Furthermore, a three-parameter discrete distribution, called the exponentiated generalized Weibull–Rayleigh distribution, is generated from this [...] Read more.

Statistical distributions play a crucial role in analyzing real data with varying behavior. In this study, the exponentiated generalized Weibull-G family is discretized using the survival discretization method. Furthermore, a three-parameter discrete distribution, called the exponentiated generalized Weibull–Rayleigh distribution, is generated from this discretized family. This distribution is flexible in modeling various data types, as evidenced by the distinct structures of its probability mass function and hazard rate function. Some statistical properties of both the family and the proposed distribution are discussed. Three estimation approaches—the maximum likelihood, the minimum chi-square, and the method of moments—are used to estimate the distribution’s parameters and are evaluated across three simulation cases. Moreover, the effectiveness of the proposed distribution is evaluated using four datasets from medicine and education. Overall, the results demonstrated the superiority of the proposed distribution fitting the examined data relative to some existing discrete models. Full article

(This article belongs to the Special Issue New Perspectives in Mathematical Statistics, 2nd Edition)

► Show Figures

Figure 1

29 pages, 564 KB

Open AccessArticle

Edgeworth Coefficients for Standard Multivariate Estimates

by Christopher Stroude Withers

Axioms 2025, 14(8), 632; https://doi.org/10.3390/axioms14080632 - 13 Aug 2025

Cited by 2 | Viewed by 830

Abstract

I give for the first time explicit formulas for the coefficients needed for the fourth-order Edgeworth expansions of a multivariate standard estimate. I call these the Edgeworth coefficients. They are Bell polynomials in the cumulant coefficients. Standard estimates include most estimates of [...] Read more.

I give for the first time explicit formulas for the coefficients needed for the fourth-order Edgeworth expansions of a multivariate standard estimate. I call these the Edgeworth coefficients. They are Bell polynomials in the cumulant coefficients. Standard estimates include most estimates of interest, including smooth functions of sample means and other empirical estimates. I also give applications to ellipsoidal and hyperrectangular sets. Full article

(This article belongs to the Special Issue New Perspectives in Mathematical Statistics, 2nd Edition)

► Show Figures

Figure 1

26 pages, 478 KB

Open AccessArticle

Treatment Effect Estimation in Survival Analysis Using Copula-Based Deep Learning Models for Causal Inference

by Jong-Min Kim

Axioms 2025, 14(6), 458; https://doi.org/10.3390/axioms14060458 - 10 Jun 2025

Cited by 4 | Viewed by 2776

Abstract

This paper presents the use of Copula-based deep learning with Horvitz–Thompson (HT) weights and inverse probability of treatment weighting (IPTW) for estimating propensity scores in causal inference problems. This study compares the performance of the statistical methods—Copula-based deep learning with HT and IPTW [...] Read more.

This paper presents the use of Copula-based deep learning with Horvitz–Thompson (HT) weights and inverse probability of treatment weighting (IPTW) for estimating propensity scores in causal inference problems. This study compares the performance of the statistical methods—Copula-based deep learning with HT and IPTW weights, propensity score matching (PSM), and logistic regression—in estimating the treatment effect (ATE) using both simulated and real-world data. Our results show that the Copula-based recurrent neural network (RNN) with the method of HT weights provides the most precise and robust treatment effect estimate, with narrow confidence intervals indicating high confidence in the results. The PSM model yields the largest treatment effect estimate, but with greater uncertainty, suggesting sensitivity to data imbalances. In contrast, logistic regression and causal forests produce a substantially smaller estimate, potentially underestimating the treatment effect, particularly in structured datasets such as COMPAS scores. Overall, copula-based methods (HT and IPTW) tend to produce higher and more precise estimates, making them effective choices for treatment effect estimation in complex settings. Our findings emphasize the importance of method selection based on both the magnitude and precision of the treatment effect for accurate analysis. Full article

(This article belongs to the Special Issue New Perspectives in Mathematical Statistics, 2nd Edition)

► Show Figures

Figure 1

Journal Menu

Journal Browser

New Perspectives in Mathematical Statistics, 2nd Edition

Share This Special Issue

Special Issue Editors

Special Issue Information

Keywords

Benefits of Publishing in a Special Issue

Published Papers (8 papers)

Research

Further Information

Guidelines

MDPI Initiatives

Follow MDPI