In this paper,the empirical likelihood confidence regions for the regression coefficient in a linear model are constructed under m-dependent errors.It is shown that the blockwise empirical likelihood is a good way to ...In this paper,the empirical likelihood confidence regions for the regression coefficient in a linear model are constructed under m-dependent errors.It is shown that the blockwise empirical likelihood is a good way to deal with dependent samples.展开更多
Let {εt;t ∈ Z} be a sequence of m-dependent B-valued random elements with mean zeros and finite second moment. {a3;j ∈ Z} is a sequence of real numbers satisfying ∑j=-∞^∞｜aj｜ 〈 ∞. Define a moving average pro...Let {εt;t ∈ Z} be a sequence of m-dependent B-valued random elements with mean zeros and finite second moment. {a3;j ∈ Z} is a sequence of real numbers satisfying ∑j=-∞^∞｜aj｜ 〈 ∞. Define a moving average process Xt = ∑j=-∞^∞aj＋tEj,t ≥ 1, and Sn = ∑t=1^n Xt,n ≥ 1. In this article, by using the weak convergence theorem of { Sn/√ n _〉 1}, we study the precise asymptotics of the complete convergence for the sequence {Xt; t ∈ N}.展开更多
For a double array of blockwise M-dependent random variables {Xmn,m ≥ 1,n ≥ 1}, ∑i^m=1 ∑^nj=1 strong laws of large numbers are established for double sums ∑m i=1 ∑j^n=1 ij, m≥ 1, n 〉 1. The main results are ob...For a double array of blockwise M-dependent random variables {Xmn,m ≥ 1,n ≥ 1}, ∑i^m=1 ∑^nj=1 strong laws of large numbers are established for double sums ∑m i=1 ∑j^n=1 ij, m≥ 1, n 〉 1. The main results are obtained for （i） random variables {Xmn, m≥ 1, n ≥ 1} being non-identically distributed but satisfy a condition on the summability condition for the moments and （ii） random variables {Xmn, m ≥ 1, n ≥ 1} being stochastically dominated. The result in Case （i） generalizes the main result of M6ricz et al. [J. Theoret. Probab., 21, 660-671 （2008）] from dyadic to arbitrary blocks, whereas the result in Case （ii） extends a result of Gut [Ann. Probab., 6, 469-482 （1978）] to the bockwise M-dependent setting. The sharpness of the results is illustrated by some examples.展开更多
In this paper, we prove a central limit theorem for m-dependent random variables under sublinear expectations. This theorem can be regarded as a generalization of Peng＇s central limit theorem.
In this paper we give an elementary and unified proof of the Hajek-Renyi inequality, and get a general version of this inequality which not only covers the all known results but also derives some new results.
In this correspondence,we establish mean convergence theorems for the maximum of normed double sums of Banach space valued random elements.Most of the results pertain to random elements which are M-dependent.We expand...In this correspondence,we establish mean convergence theorems for the maximum of normed double sums of Banach space valued random elements.Most of the results pertain to random elements which are M-dependent.We expand and improve a number of particular cases in the literature on mean convergence of random elements in Banach spaces.One of the main contributions of the paper is to simplify and improve a recent result of Li,Presnell,and Rosalsky[Journal of Mathematical Inequalities,16,117–126(2022)].A new maximal inequality for double sums of M-dependent random elements is proved which may be of independent interest.The sharpness of the results is illustrated by four examples.展开更多
The Berry-Esseen bound provides an upper bound on the Kolmogorov distance between a random variable and the normal distribution.In this paper,we establish Berry-Esseen bounds with optimal rates for self-normalized sum...The Berry-Esseen bound provides an upper bound on the Kolmogorov distance between a random variable and the normal distribution.In this paper,we establish Berry-Esseen bounds with optimal rates for self-normalized sums of locally dependent random variables,assuming only a second-moment condition.Our proof leverages Stein's method and introduces a novel randomized concentration inequality,which may also be of independent interest for other applications.Our main results have applied to self-normalized sums of m-dependent random variables and graph dependency models.展开更多
We study smoothed quantile estimator for a class of stationary processes. We obtain the convergency rates and the Bahadur representation, as well as the asymptotic normality for this estimator by the method of m-depen...We study smoothed quantile estimator for a class of stationary processes. We obtain the convergency rates and the Bahadur representation, as well as the asymptotic normality for this estimator by the method of m-dependent approximation. Our results can be used in the study of the estimation of value-at-risk(Va R) and applied to many time series which have important applications in econometrics.展开更多
With the application of the special properties of strongly stationary m-dependent series,this paper is concerned with the empirical likelihood confidence intervals of density func- tion under m-dependent series.The li...With the application of the special properties of strongly stationary m-dependent series,this paper is concerned with the empirical likelihood confidence intervals of density func- tion under m-dependent series.The limit distribution of empirical likelihood ratio statistics is given out,and the empirical likelihood confidence intervals of parameters can be constructed.A simulation study is conducted to show the finite sample performance of the empirical likelihood based method.展开更多
文摘In this paper,the empirical likelihood confidence regions for the regression coefficient in a linear model are constructed under m-dependent errors.It is shown that the blockwise empirical likelihood is a good way to deal with dependent samples.
基金supported by National Natural Science Foundation of China (No. 10571073)
文摘Let {εt;t ∈ Z} be a sequence of m-dependent B-valued random elements with mean zeros and finite second moment. {a3;j ∈ Z} is a sequence of real numbers satisfying ∑j=-∞^∞｜aj｜ 〈 ∞. Define a moving average process Xt = ∑j=-∞^∞aj＋tEj,t ≥ 1, and Sn = ∑t=1^n Xt,n ≥ 1. In this article, by using the weak convergence theorem of { Sn/√ n _〉 1}, we study the precise asymptotics of the complete convergence for the sequence {Xt; t ∈ N}.
文摘For a double array of blockwise M-dependent random variables {Xmn,m ≥ 1,n ≥ 1}, ∑i^m=1 ∑^nj=1 strong laws of large numbers are established for double sums ∑m i=1 ∑j^n=1 ij, m≥ 1, n 〉 1. The main results are obtained for （i） random variables {Xmn, m≥ 1, n ≥ 1} being non-identically distributed but satisfy a condition on the summability condition for the moments and （ii） random variables {Xmn, m ≥ 1, n ≥ 1} being stochastically dominated. The result in Case （i） generalizes the main result of M6ricz et al. [J. Theoret. Probab., 21, 660-671 （2008）] from dyadic to arbitrary blocks, whereas the result in Case （ii） extends a result of Gut [Ann. Probab., 6, 469-482 （1978）] to the bockwise M-dependent setting. The sharpness of the results is illustrated by some examples.
文摘In this paper, we prove a central limit theorem for m-dependent random variables under sublinear expectations. This theorem can be regarded as a generalization of Peng＇s central limit theorem.
基金Supported by the National Natural Science Foundation of China(10671149)
文摘In this paper we give an elementary and unified proof of the Hajek-Renyi inequality, and get a general version of this inequality which not only covers the all known results but also derives some new results.
文摘In this correspondence,we establish mean convergence theorems for the maximum of normed double sums of Banach space valued random elements.Most of the results pertain to random elements which are M-dependent.We expand and improve a number of particular cases in the literature on mean convergence of random elements in Banach spaces.One of the main contributions of the paper is to simplify and improve a recent result of Li,Presnell,and Rosalsky[Journal of Mathematical Inequalities,16,117–126(2022)].A new maximal inequality for double sums of M-dependent random elements is proved which may be of independent interest.The sharpness of the results is illustrated by four examples.
基金supported by the Singapore Ministry of Education Academic Research Fund Tier 2(Grant No.MOE2018-T2-2-076)。
文摘The Berry-Esseen bound provides an upper bound on the Kolmogorov distance between a random variable and the normal distribution.In this paper,we establish Berry-Esseen bounds with optimal rates for self-normalized sums of locally dependent random variables,assuming only a second-moment condition.Our proof leverages Stein's method and introduces a novel randomized concentration inequality,which may also be of independent interest for other applications.Our main results have applied to self-normalized sums of m-dependent random variables and graph dependency models.
文摘We study smoothed quantile estimator for a class of stationary processes. We obtain the convergency rates and the Bahadur representation, as well as the asymptotic normality for this estimator by the method of m-dependent approximation. Our results can be used in the study of the estimation of value-at-risk(Va R) and applied to many time series which have important applications in econometrics.
基金11th Five-Year Plan Social Science Project of Office of Education of Jilin Province(No.2007235)
文摘With the application of the special properties of strongly stationary m-dependent series,this paper is concerned with the empirical likelihood confidence intervals of density func- tion under m-dependent series.The limit distribution of empirical likelihood ratio statistics is given out,and the empirical likelihood confidence intervals of parameters can be constructed.A simulation study is conducted to show the finite sample performance of the empirical likelihood based method.
