PA样本回归权函数估计的一致渐近正态性

在平稳PA样本下,讨论了非参数回归模型中权函数估计的一致渐近正态性,并给出了这个估计的一致渐近正态性的收敛速度.     

相协样本分布函数光滑估计的正态逼近速度

在平稳相协样本下,讨论分布函数光滑估计的一致渐近正态性.在较合理的条件下给出了分布函数光滑估计的一致渐近正态性的收敛速度,这个速度几乎达到n~(-1/4).     

NA样本密度函数估计一致渐近正态性的收敛速度

在平稳NA样本下,讨论了未知密度函数估计的一致渐近正态性.在适当的条件下给出了该密度函数估计一致渐近正态性的收敛速度.这个速度几乎达到n^{-1/6}     

矩阵F分布渐近正态分布的一种方式(英文)

本文主要讨论矩阵F分布的一致渐近正态性.通过计算矩阵F分布和多元正态分布的Kullback-Leibler距离,找到了矩阵F分布一致渐近正态分布的条件.     

Fisher分布与F分布的一致渐近正态性

考虑了Fisher分布与F分布的一致渐近正态性.     

Gamma分布与Beta分布的一致渐近正态性

考虑了Gamma分布与Beta分布的一致渐近正态性.     

局部平稳扩散模型中时变参数的加权最小二乘估计

基于离散观测样本,利用局部线性拟合,得到了局部平稳扩散模型中时变漂移参数的加权最小二乘估计,并讨论了估计量的相合性,渐近正态性和一致收敛速度.同时,通过模拟研究说明了估计量的有效性.     

最近核邻型的光滑条件分位过程强逼近及其应用

文中证明了核邻型的光滑条件分位过程的强逼近，获得了其一致逼近速度．并由此结果推导出了光滑条件分位估计的渐近正态性、弱收敛和对数律等深刻结果．     

随机环境中具有迁入的分枝过程的时序估计量的性质

讨论时序估计量^m(c)~、m(c)期望、方差,得出估计量^2σn的渐近性质和估计量^mNc的一致渐近正态性.     

半参数面板空间滞后模型的两阶段最小二乘估计及应用

发展了一种半参数面板空间滞后模型的两阶段最小二乘估计方法.证明了参数分量估计具有渐近正态性且收敛速度为n~(-1/2),非参数分量估计在内点处具有渐近正态性,其收敛速度达到了非参数函数估计的最优收敛速度.并将方法应用于外商直接投资对劳动收入份额的影响分析.     

矩阵Г分布的一致渐近正态性

相对于两个密度函数之间的Kullback-Leibler距离,本文获得了矩阵Γ分布一致渐近正态分布的条件,由于矩阵Γ分布包含了Wishart分布,因此我们也指出了 Wishart分布一致渐近正态分布的条件．     

Asymptotic normality of fluctuations of the procedure of stochastic approximation with diffusive perturbation in a Markov medium

We consider the asymptotic normality of a continuous procedure of stochastic approximation in the case where the regression function contains a singularly perturbed term depending on the external medium described by a uniformly ergodic Markov process. Within the framework of the scheme of diffusion approximation, we formulate sufficient conditions for asymptotic normality in terms of the existence of a Lyapunov function for the corresponding averaged equation. __________ Translated from Ukrains’kyi Matematychnyi Zhurnal, Vol. 58, No. 12, pp. 1686–1692, December, 2006.     

Testing for small bias of tail index estimators

We determine the joint asymptotic normality of kernel and weighted least-squares estimators of the upper tail index of a regularly varying distribution when each estimator is a bivariate function of two parameters: the tuning parameter is motivated by possible underlying second-order behavior in regular variation, while no such behavior is assumed, and the fraction parameter determines that upper portion of the sample on which the estimator is based. Under the hypothesis that the scaled asymptotic biases of the estimators vanish uniformly in the parameter points considered, these results imply joint asymptotic normality for deviations of ratios of the estimators from 1, which in turn yield asymptotic chi-square tests for checking the small-bias hypothesis, equivalent to the constructibility of asymptotic confidence intervals. The test procedure suggests adaptive choices of the tuning and fraction parameters: data-driven (t)estimators.     

一类混合序列下分位数估计的一致渐近正态性

本文在混合序列下, 研究了分位数估计的一致渐近正态性. 在一定条件下其收敛速度达到. 所得结果可以应用到风险度量VaR分位数估计.     

A Central Limit Theorem for Non-stationary Strongly Mixing Random Fields

In this paper we extend a central limit theorem of Peligrad for uniformly strong mixing random fields satisfying the Lindeberg condition in the absence of stationarity property. More precisely, we study the asymptotic normality of the partial sums of uniformly \(\alpha \)-mixing non-stationary random fields satisfying the Lindeberg condition, in the presence of an extra dependence assumption involving maximal correlations.     

A note on the Bahadur representation of sample quantiles for α-mixing random variables

By some moment inequalities for α-mixing random variables, we prove the Bahadur representation of sample quantiles under very weak α-mixing coefficients. As application, the uniformly asymptotic normality is derived, the rate of which is near to n ^?1/6 under the given conditions.     

A note on the Bahadur representation of sample quantiles for α-mixing random variables

By some moment inequalities for α-mixing random variables, we prove the Bahadur representation of sample quantiles under very weak α-mixing coefficients. As application, the uniformly asymptotic normality is derived, the rate of which is near to n ^−1/6 under the given conditions.