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）.
The purpose of this application paper is to apply the Stein-Chen (SC) method to provide a Poisson-based approximation and corresponding total variation distance bounds in a time series context. The SC method that is u...The purpose of this application paper is to apply the Stein-Chen (SC) method to provide a Poisson-based approximation and corresponding total variation distance bounds in a time series context. The SC method that is used approximates the probability density function (PDF) defined on how many times a pattern such as <em>I<sub>t</sub></em>,<em>I<sub>t</sub></em><sub>+1</sub>,<em>I<sub>t</sub></em><sub>+2</sub> = {1 0 1} occurs starting at position t in a time series of length N that has been converted to binary values using a threshold. The original time series that is converted to binary is assumed to consist of a sequence of independent random variables, and could, for example, be a series of residuals that result from fitting any type of time series model. Note that if {1 0 1} is known to not occur, for example, starting at position <em>t</em> = 1, then this information impacts the probability that {1 0 1} occurs starting at position <em>t</em> = 2 or <em>t</em> = 3, because the trials to obtain {1 0 1} are overlapping and thus not independent, so the Poisson distribution assumptions are not met. Nevertheless, the results shown in four examples demonstrate that Poisson-based approximation (that is strictly correct only for independent trials) can be remarkably accurate, and the SC method provides a bound on the total variation distance between the true and approximate PDF.展开更多
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
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, 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 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The purpose of this application paper is to apply the Stein-Chen (SC) method to provide a Poisson-based approximation and corresponding total variation distance bounds in a time series context. The SC method that is used approximates the probability density function (PDF) defined on how many times a pattern such as <em>I<sub>t</sub></em>,<em>I<sub>t</sub></em><sub>+1</sub>,<em>I<sub>t</sub></em><sub>+2</sub> = {1 0 1} occurs starting at position t in a time series of length N that has been converted to binary values using a threshold. The original time series that is converted to binary is assumed to consist of a sequence of independent random variables, and could, for example, be a series of residuals that result from fitting any type of time series model. Note that if {1 0 1} is known to not occur, for example, starting at position <em>t</em> = 1, then this information impacts the probability that {1 0 1} occurs starting at position <em>t</em> = 2 or <em>t</em> = 3, because the trials to obtain {1 0 1} are overlapping and thus not independent, so the Poisson distribution assumptions are not met. Nevertheless, the results shown in four examples demonstrate that Poisson-based approximation (that is strictly correct only for independent trials) can be remarkably accurate, and the SC method provides a bound on the total variation distance between the true and approximate PDF.
文摘基于泰勒级数展开的近似函数法在求解非线性函数的中误差时需要进行复杂的导数计算,已有的Monte Carlo法虽然可以避免导数运算,但在模拟次数的选择上不具有客观性,且无法直接控制模拟结果。因此,将Stein两阶段法融入非线性函数的协方差传播理论中,并与Monte Carlo方法结合,设计了一套非线性函数协方差传播的Stein Monte Carlo算法流程。将该方法用于二维多项式函数和GNSS基线向量的协方差传播计算中,实验结果验证了其有效性,为非线性模型协方差传播的计算提供了一种新思路。
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 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.
