Distribution estimation with smoothed auxiliary information

Distribution estimation is very important in order to make statistical inference for parameters or its functions based on this distribution.In this work we propose an estimator of the distribution of some variable with non-smooth auxiliary information,for example,a symmetric distribution of this variable.A smoothing technique is employed to handle the non-differentiable function.Hence,a distribution can be estimated based on smoothed auxiliary information.Asymptotic properties of the distribution estimator are derived and analyzed.The distribution estimators based on our method are found to be significantly efficient than the corresponding estimators without these auxiliary information.Some simulation studies are conducted to illustrate the finite sample performance of the proposed estimators.     

Estimates for eigenvalues of stochastic matrices

It is well-known that the eigenvalues of stochastic matrices lie in the unit circle and at least one of them has the value one. Let {1, r 2 , ··· , r N } be the eigenvalues of stochastic matrix X of size N × N . We will present in this paper a simple necessary and sufficient condition for X such that |r j | < 1, j = 2, ··· , N . Moreover, such condition can be very quickly examined by using some search algorithms from graph theory.     

On Reed-Solomon Codes

The complexity of decoding the standard Reed-Solomon code is a well-known open problem in coding theory. The main problem is to compute the error distance of a received word. Using the Weil bound for character sum estimate, Li and Wan showed that the error distance can be determined when the degree of the received word as a polynomial is small. In the first part, the result of Li and Wan is improved. On the other hand, one of the important parameters of an error-correcting code is the dimension. In most cases, one can only get bounds for the dimension. In the second part, a formula for the dimension of the generalized trace Reed-Solomon codes in some cases is obtained.     

Exact maximum likelihood estimator for drift fractional Brownian motion at discrete observation

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.     

Global well-posedness of the stochastic 2D Boussinesq equations with partial viscosity

This paper deals with the stochastic 2D Boussinesq equations with partial viscosity. This is a coupled system of Navier-Stokes/Euler equations and the transport equation for temperature under additive noise. Global well-posedness result of this system under partial viscosity is proved by using classical energy estimates method.     

A NEW NONCONFORMING MIXED FINITE ELEMENT SCHEME FOR THE STATIONARY NAVIER-STOKES EQUATIONS

In this article, a new stable nonconforming mixed finite element scheme is proposed for the stationary Navier-Stokes equations, in which a new low order CrouzeixRaviart type nonconforming rectangular element is taken for approximating space for the velocity and the piecewise constant element for the pressure. The optimal order error estimates for the approximation of both the velocity and the pressure in L2-norm are established, as well as one in broken H1-norm for the velocity. Numerical experiments are given which are consistent with our theoretical analysis.     

金融风险管理中VaR度量的光滑估计效率

本文研究了金融风险管理理论中风险价值(VaR)的非参数核光滑估计和经验估计的效率问题.对非独立的时间序列损失/收益样本,在均方误差(MSE)准则的意义下引入亏量的概念,亏量越大表明估计效率越低.并利用亏量对VaR模型的核光滑估计和基于样本分位数的经验估计进行了比较,在理论上证明了VaR模型的核光滑估计优于经验估计.同时,通过计算机模拟证实了理论获得的结论.本文还对国内沪深两市上的证券投资基金进行了实证分析,计算了样本基金的VaR风险度量的经验估计和核光滑估计,并计算了样本基金基于周收益率和VaR估计的风险调整收益(RAROC)值,以此对样本基金的业绩做出了有用的评价.     

半参数回归模型小波估计的弱收敛速度

本文研究了误差为鞅差序列情形下的半参数回归模型.利用小波方法,在相当一般的条件下,得到了参数、非参数估计量的弱收敛速度.     

基于相依函数型数据非参数回归函数的稳健核估计

本文研究了基于相依函数型数据非参数回归函数的核估计.利用稳健的方法,在一定条件下获得了与i.i.d.场合下类似的估计量的几乎完全收敛速度,推广了现有文献中的相关结论.