摘要：
In this paper, we suggest an empirical likelihood -based test for the autoregressive coefficient of an integer -valued AR(1) model, i.e., INAR(1). We derive the limit distributions of the resulting test statistic under both null and alternative hypotheses. It turns out that regardless of whether the INAR process is stable or unstable, the statistic is always chi -squared distributed asymptotically under the null hypothesis, and as a result, it can offer unified inferences for the autoregressive coefficient. The performance of its finite sample is also demonstrated using simulations and an empirical example.
期刊：
Journal of Mathematical Physics,2024年65(2):021503 ISSN：0022-2488
通讯作者：
Zhang, J
作者机构：
[Zhang, Jing; Lei, Yuanjie; Zhang, J] Huazhong Univ Sci & Technol, Sch Math & Stat, Wuhan, Peoples R China.;[Zhang, Xueying] Cent China Normal Univ, Sch Math & Stat, Wuhan, Peoples R China.
通讯机构：
[Zhang, J ] H;Huazhong Univ Sci & Technol, Sch Math & Stat, Wuhan, Peoples R China.
摘要：
In this paper, we establish the existence of small-amplitude unique solutions near the Maxwellian for the Fokker-Planck-Boltzmann equation in a finite channel with specular reflection boundary conditions. The solution space we consider is denoted as Lk1LT infinity Lx1,v2, introduced in Duan et al. [Commun. Pure Appl. Math. 74(5), 932-1020 (2021)]. In addition, we investigate the long-time behavior of solutions for both hard and soft potentials.
作者机构：
[Cui, Hengjian] Capital Normal Univ, Sch Math Sci, Beijing, Peoples R China.;[Liu, Yanyan] Wuhan Univ, Sch Math & Stat, Wuhan, Hubei, Peoples R China.;[Mao, Guangcai] Cent China Normal Univ, Sch Math & Stat, Wuhan, Hubei, Peoples R China.;[Zhang, Jing] Zhongnan Univ Econ & Law, Sch Stat & Math, Wuhan, Hubei, Peoples R China.;[Zhang, Jing] Zhongnan Univ Econ & Law, Sch Stat & Math, Wuhan 430073, Hubei, Peoples R China.
通讯机构：
[Jing Zhang; Jing Zhang Jing Zhang Jing Zhang] S;School of Statistics and Mathematics, Zhongnan University of Economics and Law, Wuhan, Hubei, China
关键词：
conditional distance correlation;model-free screening;sure screening property;ultrahigh-dimensional survival data
摘要：
How to select the active variables that have significant impact on the event of interest is a very important and meaningful problem in the statistical analysis of ultrahigh-dimensional data. In many applications, researchers often know that a certain set of covariates are active variables from some previous investigations and experiences. With the knowledge of the important prior knowledge of active variables, we propose a model-free conditional screening procedure for ultrahigh dimensional survival data based on conditional distance correlation. The proposed procedure can effectively detect the hidden active variables that are jointly important but are weakly correlated with the response. Moreover, it performs well when covariates are strongly correlated with each other. We establish the sure screening property and the ranking consistency of the proposed method and conduct extensive simulation studies, which suggests that the proposed procedure works well for practical situations. Then, we illustrate the new approach through a real dataset from the diffuse large-B-cell lymphoma study S1.
作者机构：
[Meknani, Bassem; Zhang, Jun] Cent China Normal Univ, Sch Math & Stat, Wuhan, Peoples R China.;[Meknani, Bassem] Univ Freres Mentouri Constantine, Dept Math, Constantine, Algeria.;[Abdelhamid, Talaat] Menoufiya Univ, Fac Elect Engn, Phys & Math Engn Dept, Menoufia, Egypt.;[Abdelhamid, Talaat] Chinese Acad Sci, Shenzhen Inst Adv Technol, Shenzhen, Peoples R China.
通讯机构：
[Bassem Meknani] S;School of Mathematics and Statistics, Central China Normal University, Wuhan, People's Republic of China<&wdkj&>Département de Mathematiques, Université frères Mentouri Constantine, Constantine, Algeria
关键词：
Almost periodic solutions;pseudo-almost periodic solutions;integral solutions;evolution equations;nonlocal initial conditions;34C27;34K14;35B15;37L05;47J35
期刊：
Communications in Statistics - Theory and Methods,2023年52(15):5246-5259 ISSN：0361-0926
通讯作者：
Jing Zhang
作者机构：
[Mao, Guangcai] School of Mathematics and Statistics, Central China Normal University, Wuhan, Hubei, China;[Zhang, Jing] School of Statistics and Mathematics, Zhongnan University of Economics and Law, Wuhan, Hubei, China
通讯机构：
[Jing Zhang] S;School of Statistics and Mathematics, Zhongnan University of Economics and Law, Wuhan, Hubei, China
关键词：
Confidence bands;debiased estimation;hazard rate function;Kernel smoothing;survival data
期刊：
Journal of Nonparametric Statistics,2023年35(3):562-586 ISSN：1048-5252
通讯作者：
Xiaohui Liu
作者机构：
[Zhang, Jing; Li, Bo] Cent China Normal Univ, Sch Math & Stat, Wuhan, Hubei, Peoples R China.;[Wan, Xinyue; Liu, Xiaohui] Jiangxi Univ Finance & Econ, Sch Stat, Nanchang, Jiangxi, Peoples R China.;[Wan, Xinyue; Liu, Xiaohui] Jiangxi Univ Finance & Econ, Key Lab Data Sci Finance & Econ, Nanchang, Jiangxi, Peoples R China.;[Liu, Xiaohui] Jiangxi Univ Finance & Econ, Sch Stat, Nanchang 330013, Jiangxi, Peoples R China.;[Liu, Xiaohui] Jiangxi Univ Finance & Econ, Key Lab Data Sci Finance & Econ, Nanchang 330013, Jiangxi, Peoples R China.
通讯机构：
[Xiaohui Liu] S;School of Statistics, Jiangxi University of Finance and Economics, Nanchang, Jiangxi, People's Republic of China<&wdkj&>Key Laboratory of Data Science in Finance and Economics, Jiangxi University of Finance and Economics, Nanchang, Jiangxi, People's Republic of China
摘要：
The portmanteau test has been popular for diagnostic checking in time series models. Asymptotic properties of portmanteau tests have been exhaustively studied for real-valued time series model though, similar results for integer-valued autoregressive (INAR) models are not well documented, nevertheless. In view of this, we investigate the asymptotic behaviour of the Box-Pierce and Ljung-Box portmanteau tests in an INAR model. It turns out that these tests are chi-squared distributed asymptotically under mild conditions regardless of the process being stable or nearly unstable.
摘要：
Trace regression models are widely used to accommodate matrix-type covariates, such as panel data, images, genomics microarrays, etc. In this paper, we extend the trace regression to the quantile trace regression model. The optimal convergence rate of the estimator is derived under mild conditions. Some simulations are carried out for illustration. Finally, we apply the proposed method to a students' behavior data set related to personalized education. (C) 2021 Elsevier B.V. All rights reserved.
作者：
Ou-Yang, Le;Zhang, Xiao-Fei;Zhang, Jiajun;Chen, Jin;Wu, Min
期刊：
Frontiers in Genetics,2022年13:911999 ISSN：1664-8021
通讯作者：
Ou-Yang, L.
作者机构：
[Ou-Yang, Le] Guangdong Key Laboratory of Intelligent Information Processing, Shenzhen Key Laboratory of Media Security, Guangdong Laboratory of Artificial Intelligence and Digital Economy(SZ), College of Electronics and Information Engineering, Shenzhen University, Shenzhen, China;[Zhang, Xiao-Fei] School of Mathematics and Statistics and Hubei Key Laboratory of Mathematical Sciences, Central China Normal University, Wuhan, China;[Zhang, Jiajun] Guangdong Province Key Laboratory of Computational Science, School of Mathematics, Sun Yat-sen University, Guangzhou, China;[Chen, Jin] Institute for Biomedical Informatics, University of Kentucky, Lexington, KY, United States;[Wu, Min] Institute for Infocomm Research (I2R), A*STAR, Singapore, Singapore
通讯机构：
[Ou-Yang, L.] G;Guangdong Key Laboratory of Intelligent Information Processing, China
关键词：
data integration;machine learning;mathematical modelling;network modeling;single-cell omics data
期刊：
COMMUNICATIONS IN MATHEMATICAL SCIENCES,2022年20(2):359-375 ISSN：1539-6746
通讯作者：
Yin, Xiaobo
作者机构：
[Yang, Jerry Z.; Zhang, Jiwei] Wuhan Univ, Sch Math & Stat, Wuhan 430072, Peoples R China.;[Yang, Jerry Z.; Zhang, Jiwei] Wuhan Univ, Hubei Key Lab Computat Sci, Wuhan 430072, Peoples R China.;[Yin, Xiaobo] Cent China Normal Univ, Sch Math & Stat, Wuhan 430079, Peoples R China.;[Yin, Xiaobo] Cent China Normal Univ, Hubei Key Lab Math Sci, Wuhan 430079, Peoples R China.
通讯机构：
[Yin, Xiaobo] C;Cent China Normal Univ, Sch Math & Stat, Wuhan 430079, Peoples R China.;Cent China Normal Univ, Hubei Key Lab Math Sci, Wuhan 430079, Peoples R China.
摘要：
Nonparametric regression is of primary importance in many statistical applications. For the data with censored outcomes, how to construct a confidence band for a regression function is a basic issue but has limited research. We propose a procedure to construct the pointwise and simultaneous confidence bands for a regression function based on a debiased estimator, which is proposed by correcting the bias of the original kernel regression estimator. The corresponding theoretical properties such as consistency, convergence rates, and the asymptotic distribution of the proposed estimator are also derived. Furthermore, we carry out extensive simulation studies and a real data example from the German Breast Cancer study to evaluate the finite sample performance of the proposed method.
期刊：
Applied Mathematics and Computation,2020年370:124930 ISSN：0096-3003
通讯作者：
Zhang, Jing
作者机构：
[Ju, Lili; Tian, Hao] Ocean Univ China, Sch Math Sci, Qingdao 266100, Shandong, Peoples R China.;[Zhang, Jing] Cent China Normal Univ, Sch Math & Stat, Wuhan 430079, Hubei, Peoples R China.;[Zhang, Jing] Cent China Normal Univ, Hubei Key Lab Math Sci, Wuhan 430079, Hubei, Peoples R China.;[Ju, Lili] Univ South Carolina, Dept Math, Columbia, SC 29208 USA.
通讯机构：
[Zhang, Jing] C;Cent China Normal Univ, Sch Math & Stat, Wuhan 430079, Hubei, Peoples R China.;Cent China Normal Univ, Hubei Key Lab Math Sci, Wuhan 430079, Hubei, Peoples R China.
期刊：
Applied and Computational Harmonic Analysis,2020年48(2):539-569 ISSN：1063-5203
通讯作者：
Li, Huiyuan
作者机构：
[Zhang, Jing] Cent China Normal Univ, Sch Math & Stat, Wuhan 430079, Peoples R China.;[Zhang, Jing] Cent China Normal Univ, Hubei Key Lab Math Sci, Wuhan 430079, Peoples R China.;[Li, Huiyuan] Chinese Acad Sci, Inst Software, State Key Lab Comp Sci, Lab Parallel Comp, Beijing 100190, Peoples R China.;[Wang, Li-Lian] Nanyang Technol Univ, Sch Phys & Math Sci, Div Math Sci, Singapore 637371, Singapore.;[Zhang, Zhimin] Beijing Computat Sci Res Ctr, Beijing 100193, Peoples R China.
摘要：
In this paper, we introduce the prolate spheroidal wave functions (PSWFs) of real order alpha > -1 on the unit ball in arbitrary dimension, termed as ball PSWFs. They are eigenfunctions of both an integral operator, and a Sturm-Liouville differential operator. Different from existing works on multi-dimensional PSWFs, the ball PSWFs are defined as a generalization of orthogonal ball polynomials in primitive variables with a tuning parameter c > 0, through a "perturbation" of the Sturm-Liouville equation of the ball polynomials. From this perspective, we can explore some interesting intrinsic connections between the ball PSWFs and the finite Fourier and Hankel transforms. We provide an efficient and accurate algorithm for computing the ball PSWFs and the associated eigenvalues, and present various numerical results to illustrate the efficiency of the method. Under this uniform framework, we can recover the existing PSWFs by suitable variable substitutions. (C) 2018 Elsevier Inc. All rights reserved.
摘要：
In this paper we study an SLIR epidemic model with nonmonotonic incidence rate, which describes the psychological effect of certain serious diseases on the community when the number of infectives is getting larger. By carrying out a global analysis of the model and studying the stability of the disease-free equilibrium and the endemic equilibrium, we show that either the number of infective individuals tends to zero or the disease persists as time evolves. For the stochastic model, we prove the existence, uniqueness and positivity of the solution of the model. Then, we investigate the stability of the model and we prove that the infective tends asymptotically to zero exponentially almost surely as R-0 < 1. We also proved that the SLIR model has the ergodic property as the fluctuation is small, where the positive solution converges weakly to the unique stationary distribution.
期刊：
Journal of Scientific Computing,2017年70(2):451-477 ISSN：0885-7474
通讯作者：
Wang, Li-Lian
作者机构：
[Zhang, Jing] Cent China Normal Univ, Sch Math & Stat, Wuhan 430079, Peoples R China.;[Zhang, Jing] Cent China Normal Univ, Hubei Key Lab Math Sci, Wuhan 430079, Peoples R China.;[Wang, Li-Lian] Nanyang Technol Univ, Sch Phys & Math Sci, Div Math Sci, Singapore 637371, Singapore.;[Li, Huiyuan] Chinese Acad Sci, Inst Software, State Key Lab Comp Sci, Lab Parallel Comp, Beijing 100190, Peoples R China.;[Zhang, Zhimin] Beijing Computat Sci & Res Ctr, Beijing 100193, Peoples R China.
通讯机构：
[Wang, Li-Lian] N;Nanyang Technol Univ, Sch Phys & Math Sci, Div Math Sci, Singapore 637371, Singapore.
关键词：
Generalized prolate spheroidal wave functions of order \(-1\);Helmholtz equations;Optimal spectral schemes;Error analysis
摘要：
We introduce a family of generalized prolate spheroidal wave functions (PSWFs) of order
$$-1,$$
and develop new spectral schemes for second-order boundary value problems. Our technique differs from the differentiation approach based on PSWFs of order zero in Kong and Rokhlin (Appl Comput Harmon Anal 33(2):226–260,2012); in particular, our orthogonal basis can naturally include homogeneous boundary conditions without the re-orthogonalization of Kong and Rokhlin (2012). More notably, it leads to diagonal systems or direct “explicit” solutions to 1D Helmholtz problems in various situations. Using a rule optimally pairing the bandwidth parameter and the number of basis functions as in Kong and Rokhlin (2012), we demonstrate that the new method significantly outperforms the Legendre spectral method in approximating highly oscillatory solutions. We also conduct a rigorous error analysis of this new scheme. The idea and analysis can be extended to generalized PSWFs of negative integer order for higher-order boundary value and eigenvalue problems.
通讯机构：
[Ruan, Shigui] C;[Ruan, Shigui] U;Cent China Normal Univ, Sch Math & Stat, Wuhan 430079, Hubei, Peoples R China.;Univ Miami, Dept Math, Coral Gables, FL 33146 USA.
关键词：
Avian Influenza A H7N9 Virus;Transmission Dynamics;Basic Reproduction Number;Seasonal Influenza;Reassortment
摘要：
In March 2013, a novel avian-origin influenza A H7N9 virus was identified among human patients in China and a total of 124 human cases with 24 related deaths were confirmed by May 2013. From November 2013 to July 2017, H7N9 broke out four more times in China. A deterministic model is proposed to study the transmission dynamics of the avian influenza A H7N9 virus between wild and domestic birds and from birds to humans, and is applied to simulate the open data on numbers of the infected human cases and related deaths reported from March to May 2013 and from November 2013 to June 2014 by the Chinese Center for Disease Control and Prevention. The basic reproduction number ℛ0 is estimated and sensitivity analysis of ℛ0 in terms of model parameters is performed. Taking into account the fact that it broke out again from November 2014 to June 2015, from November 2015 to July 2016, and from October 2016 to July 2017, we believe that H7N9 virus has been well established in birds and will likely cause regular outbreaks in humans again in the future. Control measures for the future spread of H7N9 include (i) reducing the transmission opportunities between wild birds and domestic birds, (ii) closing or monitoring the retail live-poultry markets in the infected areas, and (iii) culling the infected domestic birds in the epidemic regions.
期刊：
Linear Algebra and its Applications,2015年483:293-308 ISSN：0024-3795
通讯作者：
Zhang, Jun
作者机构：
[Szokol, Patricia] Univ Debrecen, Inst Math, MTA DE Lendulet Funct Anal Res Grp, H-4010 Debrecen, Hungary.;[Tsai, Ming-Cheng] Natl Sun Yat Sen Univ, Dept Appl Math, Kaohsiung 80424, Taiwan.;[Zhang, Jun] Cent China Normal Univ, Sch Math & Stat, Wuhan 430079, Hubei, Peoples R China.
通讯机构：
[Zhang, Jun] C;Cent China Normal Univ, Sch Math & Stat, Wuhan 430079, Hubei, Peoples R China.
期刊：
Computational and Applied Mathematics,2015年34(3):1237-1249 ISSN：2238-3603
通讯作者：
Zhang, Jinhui
作者机构：
[Zhang, Jinhui] Cent China Normal Univ, Sch Math & Stat, Wuhan 430079, Peoples R China.;[Feng, Guangting] Hubei Univ Educ, Sch Math & Stat, Wuhan 430205, Peoples R China.
通讯机构：
[Zhang, Jinhui] C;Cent China Normal Univ, Sch Math & Stat, Wuhan 430079, Peoples R China.
关键词：
Chi-square test;Effective reproductive number;Goodness of fit;Parameter estimation
摘要：
This paper concentrates on the tuberculosis data of China from January 2005 to December 2012. We set up a mathematical model to fit those data with the goodness of fit and obtain the optimal parameter values of the model. By the Chi-square test of the statistical inference, the optimal parameter values of the model are reasonable. We get the effective reproductive number of the disease for each year, and also investigate the preventive measures to control the tuberculosis. (C) 2014 Elsevier Ltd. All rights reserved.
