变系数联立模型的局部线性广义矩变窗宽估计

在随机设计条件下,提出了一类变系数联立模型,运用局部线性广义矩变窗宽估计,对模型的变系数进行了估计,研究了估计量的大样本性质.利用概率论中大数定律和中心极限定理,证明了估计量的大样本性质,局部线性广义矩变窗宽估计具有相合性和渐进正态性.     

扩散模型中扩散系数的非参数组合估计

为了提高扩散系数估计的准确度, 我们利用动态组合时间域与状态域信息提出一个新的组合估计量. 我们发现所提组合估计量能有效估计扩散模型的扩散系数, 正如在本文中模拟所示. 在一定的条件下, 建立了估计量的渐进正态性, 并证明了时间域估计量与状态域估计量是渐进独立的. 大量的模拟展示了所提组合估计量优于单域估计量, 也优于本文所提估计量.     

扩散模型中扩散系数的非参数组合估计（英文）

为了提高扩散系数估计的准确度,我们利用动态组合时间域与状态域信息提出一个新的组合估计量.我们发现所提组合估计量能有效估计扩散模型的扩散系数,正如在本文中模拟所示.在一定的条件下,建立了估计量的渐进正态性,并证明了时间域估计量与状态域估计量是渐进独立的.大量的模拟展示了所提组合估计量优于单域估计量,也优于本文所提估计量.     

PA误差下回归函数小波估计的渐近性质（英文）

本文研究了回归函数小波估计的渐进性质的问题.利用概率不等式方法,获得了函数g(·)的小波估计量的r-阶矩相合,依概率收敛和强收敛以及渐进正态性的结果,所获的结果推广了其他混合相依下的相应结果.     

PA误差下回归函数小波估计的渐近性质

本文研究了回归函数小波估计的渐进性质的问题.利用概率不等式方法,获得了函数g(·)的小波估计量的r-阶矩相合,依概率收敛和强收敛以及渐进正态性的结果,所获的结果推广了其他混合相依下的相应结果.     

核实数据下均值的估计

文章研究基于替代与核实数据样本下总体均值的估计问题, 利用核权函数法定义了一个总体均值的估计量, 它包含了替代数据和核实数据两方面信息. 并证明了该估计量的渐进正态性, 同时给出估计量的收敛速度.     

正则矩阵回归的渐近性质（英文）

本文研究了正则化矩阵回归估计量的渐进性质等问题.利用Knight,Fu和Chatterjee,Lahiri分别关于向量回归的Lasso估计量渐近性研究方法,推广到矩阵回归,研究核范数正则化矩阵回归估计量对应的渐近性质.从而得到了核范数矩阵估计量在随机误差二阶矩存在即E|∈_i|~2 <∞的条件下的弱相合性和极限分布,以及在随机误差的低阶矩存在即E|∈_i|~α<∞,1 <α<2的条件下,核范数矩阵参数估计量的强相合性以及对应的收敛速度.     

连续时间下局部光滑统计量的a.s.收敛速度和边界效应

本文在连续时间场合研究回归函数的非参数估计量之一———局部光滑统计量的性质 .不仅给出其a.s.收敛的一个速度 ,而且证明了该统计量不受边界效应影响的优良性质 ;同时指出了在连续时间的场合 ,估计量中窗宽的选择和样本的轨道性质都对该估计量的性质产生重要的影响     

Ornstein-Uhlenbeck随机波动率模型的参数估计

本文研究了波动率过程为Ornstein-Uhlenbeck过程,且波动率过程与股票价格过程的相关系数ρ可为[0,1]中的任一数的随机波动率模型参数估计.给出了OU过程的统计性质,并利用鞅极限理论给出模型中参数的估计式,证明估计量是具有渐进正态性从而是相合的.     

关于洛伦兹曲线和基尼系数的统计推断

本文对于洛伦兹曲线的最一般定义,在无任何附加限制条件下,论证了基于样本数据所得到的洛仑兹曲线的通常估计量具有强相合性.在此基础上,证明了基尼系数和Schutz系数的通常估计量均具有强相合性.此外,导出了基尼系数估计量的渐进分布,并在此基础上给出了大样本情形下基尼系数的置信区间.     

Asymptotic Log-Harnack inequality and applications for stochastic systems of infinite memory

The asymptotic log-Harnack inequality is established for several kinds of models on stochastic differential systems with infinite memory: non-degenerate SDEs, neutral SDEs, semi-linear SPDEs, and stochastic Hamiltonian systems. As applications, the following properties are derived for the associated segment Markov semigroups: asymptotic heat kernel estimate, uniqueness of the invariant probability measure, asymptotic gradient estimate (hence, asymptotically strong Feller property), as well as asymptotic irreducibility.     

Power and exponential asymptotic forms of correlation functions

Using the Ornstein.Zernike equation, we obtain two asymptotic equations, one describing the exponential asymptotic behavior and the other describing the power asymptotic behavior of the total correlation function h(r). We show that the exponential asymptotic form is applicable only on a bounded distance interval l < r < L. The power asymptotic form is always applicable for r > L and reproduces the form of the interaction potential. In this case, as the density of a rarified gas decreases, L → l, the exponential asymptotic form vanishes, and only the power asymptotic form remains. Conversely, as the critical point is approached, L → ℞, and the applicability domain of the exponential asymptotic form increases without bound. __________ Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 156, No. 3, pp. 454–464, September, 2008.     

Operational asymptotic stochastic dominance

Levy (2016) proposes asymptotic first-degree stochastic dominance as a distribution ranking criterion for all non-satiable decision makers with infinite investment horizons. Given Levy’s setting, this paper defines and offers the equivalent distributional conditions for asymptotic second-degree stochastic dominance, as well as operational asymptotic first- and second-degree stochastic dominance. Interestingly, the operational asymptotic stochastic dominance provides a full rank over assets with lognormal returns and different means. Empirical applications show that our conditions can be readily implemented in practice.     

Asymptotic second-order consistency for two-stage estimation methodologies and its applications

We consider fixed-size estimation for a linear function of means from independent and normally distributed populations having unknown and respective variances. We construct a fixed-width confidence interval with required accuracy about the magnitude of the length and the confidence coefficient. We propose a two-stage estimation methodology having the asymptotic second-order consistency with the required accuracy. The key is the asymptotic second-order analysis about the risk function. We give a variety of asymptotic characteristics about the estimation methodology, such as asymptotic sample size and asymptotic Fisher-information. With the help of the asymptotic second-order analysis, we also explore a number of generalizations and extensions of the two-stage methodology to such as bounded risk point estimation, multiple comparisons among components between the populations, and power analysis in equivalence tests to plan the appropriate sample size for a study.     

Existence and stability of traveling wavefronts in a nonlocal diffusion equation with delay

This paper is concerned with the existence, asymptotic stability and uniqueness of traveling wavefronts in a nonlocal diffusion equation with delay. By constructing proper upper and lower solutions, the existence and asymptotic behavior of traveling wavefronts are established. Then the asymptotic stability with phase shift as well as the uniqueness up to translation of traveling wavefronts are proved by applying the idea of squeezing technique.     

Fixed-Point Theorems for Generalized Nonexpansive Mappings

Using the concept of asymptotic center we obtain the existence of fixed points having preassigned location for a wider class of asymptotic nonexpansive mappings in a uniformly convex Banach space. This generalization leads us to get a recent result of Alfuraidan and Khamsi for continuous monotone asymptotic nonexpansive mappings as well as the classical fixed-point result of Geobel and Kirk for asymptotic nonexpansive mappings in a uniformly convex Banach space. Also we prove a fixed-point theorem for order preserving continuous maps on a quasiordered closed convex subset of a uniformly convex Banach sapce having monotone norm.     

On nonoscillating solutions of Emden-Fowler-type equations

The asymptotic properties of nonoscillating solutions of Emden-Fowler-type equations of arbitrary order are considered. The paper contains the results of the study of the asymptotic properties of solutions with integer-valued asymptotics as well as of solutions arising from the rapid decrease of the coefficient of the equation. To analyze the asymptotic behavior of solutions of the equations, methods of power geometry are used.     

中立型随机泛函微分方程的稳定性

该文研究了一般中立型随机微分方程解的渐近性质,利用Lyapunov函数和上鞅收敛定理,得到 了该方程解的一些渐近稳定性、多项式渐近稳定性及指数稳定性等渐近性质,其结果涵盖并 推广了已有文献的结论。     

Propagation dynamics of a time periodic diffusion equation with degenerate nonlinearity

This paper is on study of traveling wave solutions and asymptotic spreading of a class of time periodic diffusion equations with degenerate nonlinearity. The asymptotic behavior of traveling wave solutions is investigated by using auxiliary equations and a limit process. In addition, the monotonicity and uniqueness, up to translation, of traveling wave solution with critical speed are determined by sliding method. Finally, combining super and sub-solutions and the stability of steady states, some sufficient conditions on asymptotic spreading are given, which indicates that the success or failure of asymptotic spreading are dependent on the degeneracy of nonlinearity as well as the size of compact support of initial value.     

Test for uniformity by empirical Fourier expansion

We consider a test for uniformity based on the empirical Fourier coefficients. We establish the asymptotic level, as well as the asymptotic power of this test.