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The Consistency of LSE Estimators in Partial Linear Regression Models under Mixing Random Errors

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Acta Mathematica Sinica,English Series 2024年第5期40卷 1244-1272页

作者： Yun Bao YAO Yu Tan LÜ Chao LU Wei wang xue jun wang School of Mathematical Sciences Anhui UniversityHefei 230601P.R.China School of Big Data and Artificial Intelligence Chizhou UniversityChizhou 247000P.R.China School of Big Data and Statistics Anhui UniversityHefei 230601P.R.China

In this paper,we consider the partial linear regression model y_(i)=x_(i)β^(*)+g(ti)+ε_(i),i=1,2,...,n,where(x_(i),ti)are known fixed design points,g(·)is an unknown function,andβ^(*)is an unknown parameter to be estimated,random errorsε_(i)are(α,β)-mix_(i)ng random *** p-th(p>1)mean consistency,strong consistency and complete consistency for least squares estimators ofβ^(*)and g(·)are investigated under some mild *** addition,a numerical simulation is carried out to study the finite sample performance of the theoretical ***,a real data analysis is provided to further verify the effect of the model.

关键词： (α,β)-mixing random variables partial linear regression model least squares estimator consistency

Retraction note to:RNA-binding protein CPSF6 regulates IBSP to affect pyroptosis in gastric cancer

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World Journal of Gastrointestinal Oncology 2024年第6期16卷 2865-2866页

作者： xue-jun wang Yong Liu Bin Ke Li Zhang Han Liang Department of Gastric Oncology Tianjin Medical University Cancer Institute and HospitalNational Clinical Research Center for CancerTianjin Clinical Research Center for CancerTianjin Key Laboratory of Digestive CancerTianjin 300060China

The authors have decided to retract the article published on World J Gastrointest Oncol(2023)for further consideration due to data errors and some misunderstandings in communication.

关键词： Retraction note

On Consistency of the Nearest Neighbor Estimator of the Density Function and Its Applications

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Acta Mathematica Sinica,English Series 2019年第5期35卷 703-720页

作者： Yi WU xue jun wang School of Mathematical Sciences Anhui University

In this paper, we mainly study the consistency of the nearest neighbor estimator of the density function based on asymptotically almost negatively associated samples. The weak consistency,strong consistency, uniformly strong consistency and the convergence rates are established under some mild conditions. As applications, we further investigate the strong consistency and the rate of strong consistency for hazard rate function estimator.

关键词： Nearest neighbor estimator weak consistency strong consistency uniform consistency hazard rate function estimator

Some Exponential Inequalities for Negatively Ort han t Dependent Random Variables

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Acta Mathematicae Applicatae Sinica 2020年第4期36卷 847-856页

作者： xue-jun wang Shu-he HU School of Mathematical Sciences Anhui UniversityHefei 230601China

In the paper,we establish some exponential inequalities for non-identically distributed negatively orthant dependent(NOD,for short)random *** addition,we also establish some exponential inequalities for the partial sum and the maximal partial sum of identically distributed NOD random *** an application,the Kolmogorov strong law of large numbers for identically distributed NOD random variables is *** results partially generalize or improve some known results.

关键词： negatively orthant dependent random variables exponential inequality negatively associated random variables strong law of large numbers

Complete Convergence and Complete Moment Convergence for Martingale Diference Sequence

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Acta Mathematica Sinica,English Series 2014年第1期30卷 119-132页

作者： xue jun wang Shu He HU School of Mathematical Science Anhui University

In the paper,we investigate the complete convergence and complete moment convergence for the maximal partial sum of martingale diference ***,we get the Baum–Katz-type Theorem and Hsu–Robbins-type Theorem for marting... 详细信息

关键词： Martingale diference sequence complete convergence complete moment convergence Baum–Katz-type theorem

Complete f-moment Convergence for Widely Orthant Dependent Random Variables and Its Application in Nonparametric Models

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Acta Mathematica Sinica,English Series 2019年第12期35卷 1917-1936页

作者： Chao LU Zhuang CHEN xue jun wang School of Mathematical Sciences Anhui University

In this paper,we study the complete f-moment convergence for widely orthant dependent(WOD,for short)random variables.A general result on complete f-moment convergence for arrays of rowwise WOD random variables is *** applications,we present some new results on complete f-moment convergence for WOD random *** also give an application to nonparametric regression models based onWOD errors by using the complete convergence that we ***,the choice of the fixed design points and the weight functions for the nearest neighbor estimator are proposed,and a numerical simulation is provided to verify the validity of the theoretical result.

关键词： Widely orthant dependent random variables complete f-moment convergence complete convergence complete consistency

Complete Moment Convergence for Arrays of Rowwise Widely Orthant Dependent Random Variables

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Acta Mathematica Sinica,English Series 2018年第10期34卷 1531-1548页

作者： Yi WU xue jun wang Andrew ROSALSKY School of Mathematical Sciences Anhui University Hefei 230601 P. R. China Department of Statistics University of Florida GainesviUe Florida 32611 USA

In this paper, complete moment convergence for widely orthant dependent random vari- ables is investigated under some mild conditions. For arrays of rowwise widely orthant dependent random variables, the main results extend recent results on complete convergence to complete moment convergence. These results on complete moment convergence are shown to yield new results on complete integral convergence.

关键词： Complete convergence complete moment convergence array of widely orthant dependent random variables complete integral convergence

The orientational preferences of backbones of proteins

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Chinese Science Bulletin 2006年第21期51卷 2559-2565页

作者： CHEN Ying wang jun xue Bin wang Wei National Laboratory of Solid State Microstructure Department of Physics and Institute of Biophysics Nanjing University Nanjing 210093China

The orientation between the backbone residues of proteins is defined based on the local configurations and the corresponding preferences are analyzed by *** is found that all the residue pairs have some specific preferences of *** statistical analysis is mainly concen-trated in the orientational distributions for two kinds of groupings of residues based on the hydrophobicity and secondary structural *** statistics for such two types of groupings shows different orienta-tional *** is found that for the former grouping the orientational preference is rather weak, while for the later a kind of strong orientational *** suggests that the formation of local structures and of secondary structures are highly related to the orientational preferences.

关键词：蛋白质主链定向参数选择残渣天然结构

The Bahadur Representation for Sample Quantiles Under Dependent Sequence

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Acta Mathematicae Applicatae Sinica 2019年第3期35卷 521-531页

作者： Wen-zhi YANG Shu-he HU xue-jun wang School of Mathematical Science Anhui University

On the one hand,we investigate the Bahadur representation for sample quantiles underφ-mixing sequence withφ(n)=O(n^-3)and obtain a rate as O(n-3/4 log n),*** the other hand,by relaxing the condition of mixing coeffi... 详细信息

关键词： Bahadur representation sample quantiles mixing sequence