This paper deals with the problems of consistency and strong consistency of the maximum likelihood estimators of the mean and variance of the drift fractional Brownian motions observed at discrete time instants. Both ...This paper deals with the problems of consistency and strong consistency of the maximum likelihood estimators of the mean and variance of the drift fractional Brownian motions observed at discrete time instants. Both the central limit theorem and the Berry-Ess′een bounds for these estimators are obtained by using the Stein’s method via Malliavin calculus.展开更多
We introduce a factorized Smith method(FSM)for solving large-scale highranked T-Stein equations within the banded-plus-low-rank structure framework.To effectively reduce both computational complexity and storage requi...We introduce a factorized Smith method(FSM)for solving large-scale highranked T-Stein equations within the banded-plus-low-rank structure framework.To effectively reduce both computational complexity and storage requirements,we develop techniques including deflation and shift,partial truncation and compression,as well as redesign the residual computation and termination condition.Numerical examples demonstrate that the FSM outperforms the Smith method implemented with a hierarchical HODLR structured toolkit in terms of CPU time.展开更多
We consider a Markov chain X = {Xi, i = 1, 2,...} with the state space {0, 1}, and define W = ∑1=1^x XiXi＋1, which is the number of 2-runs in X before time n ＋ 1. In this paper, we prove that the negative binomial ...We consider a Markov chain X = {Xi, i = 1, 2,...} with the state space {0, 1}, and define W = ∑1=1^x XiXi＋1, which is the number of 2-runs in X before time n ＋ 1. In this paper, we prove that the negative binomial distribution is an appropriate approximation for LW when VarW is greater than EW. The error estimate obtained herein improves the corresponding result in previous literatures.展开更多
In this paper, we obtain the Berry-Esseen bound for identically distributed random variables by Stein method. The results obtained generalize the results of Shao and Su （2006） and Stein （1986）.
Let Tn be the number of triangles in the random intersection graph G(n,m,p).When the mean of Tn is bounded,we obtain an upper bound on the total variation distance between Tn and a Poisson distribution.When the mean o...Let Tn be the number of triangles in the random intersection graph G(n,m,p).When the mean of Tn is bounded,we obtain an upper bound on the total variation distance between Tn and a Poisson distribution.When the mean of Tn tends to infinity,the Stein–Tikhomirov method is used to bound the error for the normal approximation of Tn with respect to the Kolmogorov metric.展开更多
A general exchange pair approach is developed to identify the limiting distribution for any sequence of random variables, by calculating the conditional mean and the conditional second moments. The error of approximat...A general exchange pair approach is developed to identify the limiting distribution for any sequence of random variables, by calculating the conditional mean and the conditional second moments. The error of approximation is also studied. In particular, a Berry-Esseen type bound of O(n^(-3/4)) is obtained for the Curie-Weiss model at the critical temperature.展开更多
In this paper, we study the count of head runs up to a fixed time in a two-state stationary Markov chain. We prove that in total variance distance, the negative binomial, Poisson and binomial distributions are appropr...In this paper, we study the count of head runs up to a fixed time in a two-state stationary Markov chain. We prove that in total variance distance, the negative binomial, Poisson and binomial distributions are appropriate approximations according to the relation of the variance and mean of the count, generalizing earlier results in previous literatures. The proof is based on Stein's method and coupling.展开更多
Let{Xk,i;k≥1,i≥1}be an array of random variables,{Xk;k≥1}be a strictly stationaryα-mixing sequence,where Xk=(Xk,1,Xk,2,...).Let{pn;n≥1}be a sequence of positive integers such that c1≤p n n≤c2,where c1,c2>0.I...Let{Xk,i;k≥1,i≥1}be an array of random variables,{Xk;k≥1}be a strictly stationaryα-mixing sequence,where Xk=(Xk,1,Xk,2,...).Let{pn;n≥1}be a sequence of positive integers such that c1≤p n n≤c2,where c1,c2>0.In this paper,we obtain the asymptotic distributions of the largest entries Ln=max1≤i<j≤pn|ρ(n)ij|of the sample correlation matrices,whereρ(n)ij denotes the Pearson correlation coefficient between X(i)and X(j),X(i)=(X1,i,X2,i,...).The asymptotic distributions of Ln is derived by using the Chen–Stein Poisson approximation method.展开更多
In this paper,a new technique is introduced to obtain non-uniform Berry-Esseen bounds for normal and nonnormal approximations by unbounded exchangeable pairs.This technique does not rely on the concentration inequalit...In this paper,a new technique is introduced to obtain non-uniform Berry-Esseen bounds for normal and nonnormal approximations by unbounded exchangeable pairs.This technique does not rely on the concentration inequalities developed by Chen and Shao[4,5]and can be applied to the quadratic forms and the general Curie-Weiss model.展开更多
In this paper, first, we present the comparison theorem and the (generalized) Stein-Rosenberg theorem for the GMPOR method, which improves some recent results([9,11,13]). Second, we also give the convergent theorem of...In this paper, first, we present the comparison theorem and the (generalized) Stein-Rosenberg theorem for the GMPOR method, which improves some recent results([9,11,13]). Second, we also give the convergent theorem of the GMPOR method, which generalizes the corresponding result of [9]. Finally, we provide the real interval such that the generalized extrapolated Jacobi iterative method and the generalized SOR methods simultaneously converge, one of the main results in [1] is extended.展开更多
研究了一般大型Stein矩阵方程的全局Krylov子空间算法.基于全局Hessenberg过程,提出了位移型全局Hess方法(shifted global Hessenberg method)和位移型全局CMRH方法(shifted global CMRH method),并给出了残差估计.数值实验表明了新方...研究了一般大型Stein矩阵方程的全局Krylov子空间算法.基于全局Hessenberg过程,提出了位移型全局Hess方法(shifted global Hessenberg method)和位移型全局CMRH方法(shifted global CMRH method),并给出了残差估计.数值实验表明了新方法相对于位移型全局Arnoldi型方法而言,在CPU时间和迭代步数上占有一定的优势.展开更多
基金supported by the National Science Foundations (DMS0504783 DMS0604207)National Science Fund for Distinguished Young Scholars of China (70825005)
文摘This paper deals with the problems of consistency and strong consistency of the maximum likelihood estimators of the mean and variance of the drift fractional Brownian motions observed at discrete time instants. Both the central limit theorem and the Berry-Ess′een bounds for these estimators are obtained by using the Stein’s method via Malliavin calculus.
基金Supported partly by NSF of China(Grant No.11801163)NSF of Hunan Province(Grant Nos.2021JJ50032,2023JJ50164 and 2023JJ50165)Degree&Postgraduate Reform Project of Hunan University of Technology and Hunan Province(Grant Nos.JGYB23009 and 2024JGYB210).
文摘We introduce a factorized Smith method(FSM)for solving large-scale highranked T-Stein equations within the banded-plus-low-rank structure framework.To effectively reduce both computational complexity and storage requirements,we develop techniques including deflation and shift,partial truncation and compression,as well as redesign the residual computation and termination condition.Numerical examples demonstrate that the FSM outperforms the Smith method implemented with a hierarchical HODLR structured toolkit in terms of CPU time.
基金Supported by National Natural Science Foundation of China(Grant No.11071021)
文摘We consider a Markov chain X = {Xi, i = 1, 2,...} with the state space {0, 1}, and define W = ∑1=1^x XiXi＋1, which is the number of 2-runs in X before time n ＋ 1. In this paper, we prove that the negative binomial distribution is an appropriate approximation for LW when VarW is greater than EW. The error estimate obtained herein improves the corresponding result in previous literatures.
基金Supported by the National Natural Science Foundation of China (11101364)the Zhejiang Natural Science Foundation of China (Y6110110)
文摘In this paper, we obtain the Berry-Esseen bound for identically distributed random variables by Stein method. The results obtained generalize the results of Shao and Su （2006） and Stein （1986）.
文摘Let Tn be the number of triangles in the random intersection graph G(n,m,p).When the mean of Tn is bounded,we obtain an upper bound on the total variation distance between Tn and a Poisson distribution.When the mean of Tn tends to infinity,the Stein–Tikhomirov method is used to bound the error for the normal approximation of Tn with respect to the Kolmogorov metric.
基金supported by Hong Kong Research Grants Council General Research Fund (Grant Nos. 403513 and 14302515)
文摘A general exchange pair approach is developed to identify the limiting distribution for any sequence of random variables, by calculating the conditional mean and the conditional second moments. The error of approximation is also studied. In particular, a Berry-Esseen type bound of O(n^(-3/4)) is obtained for the Curie-Weiss model at the critical temperature.
基金supported by National Natural Science Foundation of China (Grant No. 11071021)
文摘In this paper, we study the count of head runs up to a fixed time in a two-state stationary Markov chain. We prove that in total variance distance, the negative binomial, Poisson and binomial distributions are appropriate approximations according to the relation of the variance and mean of the count, generalizing earlier results in previous literatures. The proof is based on Stein's method and coupling.
基金National Natural Science Foundation of China(Grant Nos.11771178 and 12171198)the Science and Technology Development Program of Jilin Province(Grant No.20210101467JC)+1 种基金Science and Technology Program of Jilin Educational Department during the“13th Five-Year”Plan Period(Grant No.JJKH20200951KJ)Fundamental Research Funds for the Central Universities。
文摘Let{Xk,i;k≥1,i≥1}be an array of random variables,{Xk;k≥1}be a strictly stationaryα-mixing sequence,where Xk=(Xk,1,Xk,2,...).Let{pn;n≥1}be a sequence of positive integers such that c1≤p n n≤c2,where c1,c2>0.In this paper,we obtain the asymptotic distributions of the largest entries Ln=max1≤i<j≤pn|ρ(n)ij|of the sample correlation matrices,whereρ(n)ij denotes the Pearson correlation coefficient between X(i)and X(j),X(i)=(X1,i,X2,i,...).The asymptotic distributions of Ln is derived by using the Chen–Stein Poisson approximation method.
基金supported by National Key R&D Program of China(2018YFA0703900)the Na-tional Natural Science Foundation of China(11701331)+1 种基金Shandong Provincial Natural Science Founda-tion(ZR2017QA007)Young Slcholars Program of Shandong University。
文摘In this paper,a new technique is introduced to obtain non-uniform Berry-Esseen bounds for normal and nonnormal approximations by unbounded exchangeable pairs.This technique does not rely on the concentration inequalities developed by Chen and Shao[4,5]and can be applied to the quadratic forms and the general Curie-Weiss model.
基金This research is supported by the National Key R&D Program of China(Grant Nos.2020YFA0712700,2018YFA0703901)National Natural Science Foundation of China(Grant Nos.11871458,11688101)Key Research Program of Frontier Sciences,CAS(Grant No.QYZDB-SSW-SYS017).
文摘Peng,S.[6]proved the law of large numbers under a sublinear expectation.In this paper,we give its error estimates by Stein’s method.
文摘In this paper, first, we present the comparison theorem and the (generalized) Stein-Rosenberg theorem for the GMPOR method, which improves some recent results([9,11,13]). Second, we also give the convergent theorem of the GMPOR method, which generalizes the corresponding result of [9]. Finally, we provide the real interval such that the generalized extrapolated Jacobi iterative method and the generalized SOR methods simultaneously converge, one of the main results in [1] is extended.
文摘研究了一般大型Stein矩阵方程的全局Krylov子空间算法.基于全局Hessenberg过程,提出了位移型全局Hess方法(shifted global Hessenberg method)和位移型全局CMRH方法(shifted global CMRH method),并给出了残差估计.数值实验表明了新方法相对于位移型全局Arnoldi型方法而言,在CPU时间和迭代步数上占有一定的优势.
