线性随机场的经验周期图的中偏差（英文）

在本文中,我们证明了线性随机场的二次形和经验周期图的中偏差.关于线性随机场的主要假设是驱动随机变量的对数Sobolev不等式和谱密度的一些可积条件.作为统计应用,我们给出了单边自回归平稳场的最小二乘估计和Yule-Walker估计的中偏估差计.上述结论是对文献[8]中线性随机过程的结论的推广.     

半参数非线性回归模型渐近推断的几何

本文利用Severini和Wong^[1]提出的最佳偏差曲线的概念,对半参数非线性回归模型建立了类似于Bates和Watts^[2]的几何结构。利用这个几何结构,我们研究了与统计曲率有关的某些渐近推断。文献中的许多结果^[3-6]被推广到半参数非线性回归模型。     

一类正值线性过程的参数估计

在研究水质污染问题时,文[1]提出了非负一阶自回归模型:X_t=(?)X_(t-1)+ξ_t,其中{ξ_t}为独立同分布非负随机序列,0<(?)<1.此模型中 X_t 表示在时刻 t 时净化池中的污水量,1-(?)_1表示在单位时间间隔内被净化污水的比例,ξ_t 表示在时刻 t 注入净化池中的污水量.文[1]给出了模型参数的极为简便的强相合估计和相应的模拟结果.文[2]把[1]的结果推广到二阶自回归情形,克服了本质上的困难获得相应的结果.本文提出一类更为广泛的正值线性模型     

关于一类解析函数的性质

引进用Hλ算子定义的一类解析函数Pλ(μ,α,β).我们导出该类中函数的积分表达式,证明偏差定理,并推广了文[3]中的主要结果.同时改进了[4]中的一个不等式.     

关于AR（P）模型参数的LAD估计收敛性

一、引言和定理的叙述由于在实际问题中,具有无限方差的误差可能适合许多现象(参看[1]—[4]),所以估计下述自回归模型(1.1)的回归参数有重大的意义.     

周期相关时间序列与周期自回归模型

介绍了周期相关时间序列和周期自回归模型,并研究了周期自回归时间序列的稳定性及周期性,得到了它为周期相关时间序列的一个充要条件,推广了文献[1]的结论.     

一阶具偏差变元微分方程的强迫振动

1.引言 关于一阶具偏差变元微分方程的解的振动性质已有广泛的讨论,新书[2]中总结了直到1984年的主要成果,也可参看综述文章[6]。但对于具有强迫项的一阶具偏差变元微分方程的振动性质结果很少,作者仅见到Tomaras的工作他研究方程     

某种一般非参数回归函数估计的强相合

本文研究了较为一般的非参数回归函数估计的问题.利用传输不等式,获得了参数估计的强相合性,推广了文献[1]、[6]等结果.     

可加稳定过程的自相交局部时

本文研究了可加稳定过程的自相交局部时的问题.利用Borel–Canteil引理等方法,得到可加稳定过程的自相交局部时的Hlder上界,推广了文献[5]中的结果.     

算子方法在单叶函数中的应用

<正> 随着对单叶函数偏差定理研究的深入,人们越来越深刻地认识到偏差定理在解决单叶函数的各种极值问题,特别在系数估计中的重要作用.因此有不少作者从事这方面的研究.最近在[10]中,用连续函数空间上的线性泛函分析的方法研究偏差定理,获得了相当深刻的结果.     

Moderate deviations of generalized method of moments and empirical likelihood estimators

This paper studies moderate deviation behaviors of the generalized method of moments and generalized empirical likelihood estimators for generalized estimating equations, where the number of equations can be larger than the number of unknown parameters. We consider two cases for the data generating probability measure: the model assumption and local contaminations or deviations from the model assumption. For both cases, we characterize the first-order terms of the moderate deviation error probabilities of these estimators. Our moderate deviation analysis complements the existing literature of the local asymptotic analysis and misspecification analysis for estimating equations, and is useful to evaluate power and robust properties of statistical tests for estimating equations which typically involve some estimators for nuisance parameters.     

Moderate deviation principle for autoregressive processes

A moderate deviation principle for autoregressive processes is established. As statistical applications we provide the moderate deviation estimates of the least square and the Yule–Walker estimators of the parameter of an autoregressive process. The main assumption on the autoregressive process is the Gaussian integrability condition for the noise, which is weaker than the assumption of Logarithmic Sobolev Inequality in [H. Djellout, A. Guillin, L. Wu, Moderate deviations of empirical periodogram and nonlinear functionals of moving average processes, Ann. I. H. Poincaré-PR 42 (2006) 393–416].     

Deviation inequalities and moderate deviations for estimators of parameters in TAR models

In this paper, we establish some deviation inequalities and the moderate deviation principles for the least squares estimators of the parameters in the threshold autoregressive model under the assumption that the noise random variable satisfies a logarithmic Sobolev inequality.     

Parallel Algorithms and Probability of Large Deviation for Stochastic Convex Optimization Problems

We consider convex stochastic optimization problems under different assumptions on the properties of available stochastic subgradient. It is known that, if the value of the objective function is available, one can obtain, in parallel, several independent approximate solutions in terms of the objective residual expectation. Then, choosing the solution with the minimum function value, one can control the probability of large deviation of the objective residual. On the contrary, in this short paper, we address the situation, when the value of the objective function is unavailable or is too expensive to calculate. Under "‘light-tail"’ assumption for stochastic subgradient and in general case with moderate large deviation probability, we show that parallelization combined with averaging gives bounds for probability of large deviation similar to a serial method. Thus, in these cases, one can benefit from parallel computations and reduce the computational time without loss in the solution quality.     

Large deviations of realized volatility

This paper studies large and moderate deviation properties of a realized volatility statistic of high frequency financial data. We establish a large deviation principle for the realized volatility when the number of high frequency observations in a fixed time interval increases to infinity. Our large deviation result can be used to evaluate tail probabilities of the realized volatility. We also derive a moderate deviation rate function for a standardized realized volatility statistic. The moderate deviation result is useful for assessing the validity of normal approximations based on the central limit theorem. In particular, it clarifies that there exists a trade-off between the accuracy of the normal approximations and the path regularity of an underlying volatility process. Our large and moderate deviation results complement the existing asymptotic theory on high frequency data. In addition, the paper contributes to the literature of large deviation theory in that the theory is extended to a high frequency data environment.     

Moderate Deviation for the Rightmost Position in a Branching Brownian Motion

We study the moderate deviation probability of the position of the rightmost particle in a branching Brownian motion and obtain its moderate deviation function. Firstly, Chauvin and Rouault studied the large deviation probability for the rightmost position in a branching Brownian motion. Recently, Derrida and Shiconsidered lower deviation for the same model. By contrast, Our main result is more extensive.     

带小随机扰动的中偏差原理(英文)

本文研究了带小随机扰动的中偏差原理.运用收缩原理和指数逼近方法,Freidlin-Wentzell定理给出了Xε的大偏差原理,从而得到了Xε的中偏差原理.     

Moderate Deviations for Longest Increasing Subsequences: The Lower Tail

We derive a moderate deviation principle for the lower tail probabilities of the length of a longest increasing subsequence in a random permutation. It refers to the regime between the lower tail large deviation regime and the central limit regime. The present article together with the upper tail moderate deviation principle in Ref. 12 yields a complete picture for the whole moderate deviation regime. Other than in Ref. 12, we can directly apply estimates by Baik, Deift, and Johansson, who obtained a (non-standard) Central Limit Theorem for the same quantity.     

Asymptotic Normality of Autoregressive Processes

In the present paper, the form of iterated limits of the moderate deviation principle for dependent variables is considered and as an application, the moderate deviation principle of m-dependent random variables is obtained.     

次线性期望下独立随机变量列的大偏差和中偏差

本文研究在次线性期望下的独立随机变量列的大偏差和中偏差原理. 利用次可加方法, 我们得 到次线性期望下的大偏差原理. 与次线性期望下的中心极限定理相应的中偏差原理也被建立.