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Mathematics
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Statistical Theory and Application
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Statistical Theory and Application

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

Deadline for manuscript submissions: closed (20 October 2023) | Viewed by 11283

Special Issue Editor

Prof. Dr. Xuejun Wang

E-Mail Website
Guest Editor
School of Big Data and Statistics, Anhui University, Hefei 230601, China
Interests: probability limit theory; dependent sequence; mathematical statistics
Special Issues, Collections and Topics in MDPI journals

Special Issue Information

Dear Colleagues,

Nowadays, statistical theory and method are becoming more and more important, in big data and machine learning, for example. Statistical research includes statistical models, statistical methods, statistical estimation, statistical inference, statistical applications, and so on.

This Special Issue invites papers on statistical theory and its application in economics, finance, and biology, among others. For example, the topics of nonparametric statistics, parametric statistics, semiparametric statistics, multivariate analysis, regression analysis, time series analysis, probability limit theorems, statistics and computation, and so on, are encouraged to make theoretical and methodological advances in probability and statistics.

Research papers, review articles, and short communications are invited. 

Topics of interest include but are not limited to the following:

  • regression analysis;
  • nonparametric statistics;
  • semiparametric statistics;
  • multivariate analysis
  • Computational statistics;
  • High dimensional statistics;
  • probability limit theorems.

Prof. Dr. Xuejun Wang
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 100 words) can be sent to the Editorial Office for announcement on this website.

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-blind 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.

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Related Special Issue

Published Papers (5 papers)

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Research

16 pages, 502 KiB  
Article
Wild Bootstrap-Based Bias Correction for Spatial Quantile Panel Data Models with Varying Coefficients
by Xiaowen Dai, Shidan Huang, Libin Jin and Maozai Tian
Mathematics 2023, 11(9), 2005; https://doi.org/10.3390/math11092005 - 23 Apr 2023
Viewed by 1435
Abstract
This paper studies quantile regression for spatial panel data models with varying coefficients, taking the time and location effects of the impacts of the covariates into account, i.e., the implications of covariates may change over time and location. Smoothing methods are employed for [...] Read more.
This paper studies quantile regression for spatial panel data models with varying coefficients, taking the time and location effects of the impacts of the covariates into account, i.e., the implications of covariates may change over time and location. Smoothing methods are employed for approximating varying coefficients, including B-spline and local polynomial approximation. A fixed-effects quantile regression (FEQR) estimator is typically biased in the presence of the spatial lag variable. The wild bootstrap method is employed to attenuate the estimation bias. Simulations are conducted to study the performance of the proposed method and show that the proposed methods are stable and efficient. Further, the estimators based on the B-spline method perform much better than those of the local polynomial approximation method, especially for location-varying coefficients. Real data about economic development in China are also analyzed to illustrate application of the proposed procedure. Full article
(This article belongs to the Special Issue Statistical Theory and Application)
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14 pages, 548 KiB  
Article
K-L Estimator: Dealing with Multicollinearity in the Logistic Regression Model
by Adewale F. Lukman, B. M. Golam Kibria, Cosmas K. Nziku, Muhammad Amin, Emmanuel T. Adewuyi and Rasha Farghali
Mathematics 2023, 11(2), 340; https://doi.org/10.3390/math11020340 - 9 Jan 2023
Cited by 7 | Viewed by 3651
Abstract
Multicollinearity negatively affects the efficiency of the maximum likelihood estimator (MLE) in both the linear and generalized linear models. The Kibria and Lukman estimator (KLE) was developed as an alternative to the MLE to handle multicollinearity for the linear regression model. In this [...] Read more.
Multicollinearity negatively affects the efficiency of the maximum likelihood estimator (MLE) in both the linear and generalized linear models. The Kibria and Lukman estimator (KLE) was developed as an alternative to the MLE to handle multicollinearity for the linear regression model. In this study, we proposed the Logistic Kibria-Lukman estimator (LKLE) to handle multicollinearity for the logistic regression model. We theoretically established the superiority condition of this new estimator over the MLE, the logistic ridge estimator (LRE), the logistic Liu estimator (LLE), the logistic Liu-type estimator (LLTE) and the logistic two-parameter estimator (LTPE) using the mean squared error criteria. The theoretical conditions were validated using a real-life dataset, and the results showed that the conditions were satisfied. Finally, a simulation and the real-life results showed that the new estimator outperformed the other considered estimators. However, the performance of the estimators was contingent on the adopted shrinkage parameter estimators. Full article
(This article belongs to the Special Issue Statistical Theory and Application)
19 pages, 430 KiB  
Article
Homogeneity Test of Multi-Sample Covariance Matrices in High Dimensions
by Peng Sun, Yincai Tang and Mingxiang Cao
Mathematics 2022, 10(22), 4339; https://doi.org/10.3390/math10224339 - 18 Nov 2022
Viewed by 1619
Abstract
In this paper, a new test statistic based on the weighted Frobenius norm of covariance matrices is proposed to test the homogeneity of multi-group population covariance matrices. The asymptotic distributions of the proposed test under the null and the alternative hypotheses are derived, [...] Read more.
In this paper, a new test statistic based on the weighted Frobenius norm of covariance matrices is proposed to test the homogeneity of multi-group population covariance matrices. The asymptotic distributions of the proposed test under the null and the alternative hypotheses are derived, respectively. Simulation results show that the proposed test procedure tends to outperform some existing test procedures. Full article
(This article belongs to the Special Issue Statistical Theory and Application)
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7 pages, 467 KiB  
Article
Joint Models for Incomplete Longitudinal Data and Time-to-Event Data
by Yuriko Takeda, Toshihiro Misumi and Kouji Yamamoto
Mathematics 2022, 10(19), 3656; https://doi.org/10.3390/math10193656 - 6 Oct 2022
Viewed by 1866
Abstract
Clinical studies often collect longitudinal and time-to-event data for each subject. Joint modeling is a powerful methodology for evaluating the association between these data. The existing models, however, have not sufficiently addressed the problem of missing data, which are commonly encountered in longitudinal [...] Read more.
Clinical studies often collect longitudinal and time-to-event data for each subject. Joint modeling is a powerful methodology for evaluating the association between these data. The existing models, however, have not sufficiently addressed the problem of missing data, which are commonly encountered in longitudinal studies. In this paper, we introduce a novel joint model with shared random effects for incomplete longitudinal data and time-to-event data. Our proposed joint model consists of three submodels: a linear mixed model for the longitudinal data, a Cox proportional hazard model for the time-to-event data, and a Cox proportional hazard model for the time-to-dropout from the study. By simultaneously estimating the parameters included in these submodels, the biases of estimators are expected to decrease under two missing scenarios. We estimated the proposed model by Bayesian approach, and the performance of our method was evaluated through Monte Carlo simulation studies. Full article
(This article belongs to the Special Issue Statistical Theory and Application)
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19 pages, 2164 KiB  
Article
Spatial Outlier Accommodation Using a Spatial Variance Shift Outlier Model
by Ali Mohammed Baba, Habshah Midi and Nur Haizum Abd Rahman
Mathematics 2022, 10(17), 3182; https://doi.org/10.3390/math10173182 - 3 Sep 2022
Cited by 2 | Viewed by 1345
Abstract
Outlier detection has been a long-debated subject among researchers due to its effect on model fitting. Spatial outlier detection has received considerable attention in the recent past. On the other hand, outlier accommodation, particularly in spatial applications, retains vital information about the model. [...] Read more.
Outlier detection has been a long-debated subject among researchers due to its effect on model fitting. Spatial outlier detection has received considerable attention in the recent past. On the other hand, outlier accommodation, particularly in spatial applications, retains vital information about the model. It is pertinent to develop a method that is capable of accommodating detected spatial outliers in a fashion that retains vital information in the spatial models. In this paper, we formulate the variance shift outlier model (SVSOM) in the spatial regression as a robust spatial model using restricted maximum likelihood (REML) and use weights based on the detected outliers in the model. The spatial outliers are accommodated via a revised model for the outlier observations with the help of the SVSOM. Simulation results show that the SVSOM, based on the detected spatial outliers is more efficient than the general spatial model (GSM). The findings of this study also reveal that contamination in the residuals and x variable have little effect on the parameter estimates of the SVSOM, and that outliers in the y variable are always detectable. Asymptotic distribution of the squared spatial prediction residuals are obtained to confirm the outlyingness of an observation. The merit of or proposed SVSOM for the detection and accommodating outliers is also confirmed using artificial and COVID-19 data sets. Full article
(This article belongs to the Special Issue Statistical Theory and Application)
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