相依样本下污染线性模型的最近邻估计

考虑一般线性模型,设误差序列{ei}是平稳的α-混合序列,具有公共未知密度,f(x)．本文首先讨论了基于残差的f(x)的最近邻估计的相合性及收敛速度,然后把结论推广到污染线性模型,讨论了污染系数ε,误差的主体分布及回归系数β的估计的相合性,收敛速度以及(β|^)的渐近正态性．     

半参数方差误差模型的估计

本文综合近邻权函数法及最小二乘法，用两阶段最小二乘估计的方法得到了半参数EV模型中参数的估计量及其强相合性，渐近正态性。同时也得到了非参数函数的估计量及其强相合性，一致强相合性。     

有重复观测时变系数线性结构关系EV模型的参数估计

利用重复观测数据和加权方法给出了有重复观测时变系数一维线性结构关系EV模型中的参数估计,证明了估计的弱相合性和强相合性．     

混合整数线性模型参数最小二乘估计的弱相合性

在GPS和测绘等领域中,混合整数线性模型是非常重要的一种模型。本文在混合整数线性模型参数的最小二乘估计的基础上,证明了该估计量的弱相合性。Monte Carlo模拟验证表明,各参数估计的相合效果明显。     

变系数线性结构关系EV模型的参数估计

利用加权正交回归最小二乘法给出了变系数一维线性结构关系EV模型中的参数 估计,证明了估计的弱相合性和强相合性.     

M-估计下误差密度核估计的相合性

线性模型Yi=x′iβ ei,i=1,2…，其中{ei}i^∞=1,i.i.d.,有未知密度f(x），本文讨论了在对β作一般M－估计后，基于残差做出的误差密度核估计的相合性，在比文献弱的条件下，证明了误差密度核估计的逐点弱相合，逐点强相合和一致强相合。     

拟似然非线性模型中MQLE的弱相合性的充分条件

拟似然非线性模型包括广义线性模型作为一个特殊情形.给出了拟似然非线性模型中极大拟似然估计的弱相合性的一些充分条件,其中矩的条件要弱于文献中极大拟似然估计的强相合性的条件.     

自变量可重复观测的线性EV模型

研究了仅自变量可以做重复观测的线性EV模型, 构造了模型回归系数的估计, 并在适当条件下证明了估计量的相合性和渐近正态性. 所得结果揭示了与自变量和因变量同步重复观测模型的差异.     

关于线性模型回归系数LS估计的相合性

当误差项是不相关随机变量时[1]和[2]给出了线性模型中回归系数最小二乘估计弱相合性的充要条件。我们把这一结果推广到具有平稳随机误差项的线性模型。     

再论线性模型自变元选择的BIC方法相容性条件

在许多情况下，对线性回归模型我们感兴趣于选择足够多的重要预测变量，本文指出了１中对著名的ＢＩＣ准则变量选择方法强相合性证明的错误，并重新给出了一组强相全性条件。在这组条件下，我们也证明了ＢＩＣ选择方法是强相合的，这组新的条件既容易验证又应用广泛。     

RECENT PROGRESS ON SPHERICAL HARMONIC APPROXIMATION MADE BY BNU RESEARCH GROUP ——In memory of Professor Sun Yongsheng

As early as in 1990, Professor Sun Yongsheng, suggested his students at Beijing Normal University to consider research problems on the unit sphere. Under his guidance and encouragement his students started the research on spherical harmonic analysis and approximation. In this paper, we incompletely introduce the main achievements in this area obtained by our group and relative researchers during recent 5 years （2001-2005）. The main topics are： convergence of Cesaro summability, a.e. and strong summability of Fourier-Laplace series; smoothness and K-functionals; Kolmogorov and linear widths.     

A unified approach to certain problems of best local approximation

In this paper we study best local quasi-rational approximation and best local approximation from finite dimensional subspaces of vectorial functions of several variables. Our approach extends and unifies several problems concerning best local multi-point approximation in different norms.     

Boundedness for commutators of multipliers on Hardy type spaces

In this paper, we study the commutators generalized by multipliers and a BMO function. Under some assumptions, we establish its boundedness properties from certain atomic Hardy space Hb^p（R^n） into the Lebesgue space L^p with p 〈 1.     

THE 8~(th) INTERNATIONAL CONGRESS ON INDUSTRIAL AND APPLIED MATHEMATICS

<正>August 10-14,2015Beijing,ChinaThe International Congress on Industrial and Applied Mathematics(ICIAM)is the premier international congress in the field of applied mathematics held every four years under the auspices of the International Council for Industrial and Applied Mathematics.From August 10 to 14,2015,mathematicians,scientists     

Towards Excellence in Science Chinese Academy of Sciences

<正>May 26,2014,Beijing Science is a human enterprise in the pursuit of knowledge.The scientific revolution that occurred in the 17th Century initiated the advances of modern science.The scientific knowledge system created by     

Bounds for the zeros of polynomials

Let P(z)=∑↓j=0↑n ajx^j be a polynomial of degree n. In this paper we prove a more general result which interalia improves upon the bounds of a class of polynomials. We also prove a result which includes some extensions and generalizations of Enestrǒm-Kakeya theorem.     

Boundedness of commutators related to Marcinkiewicz integrals on hardy type spaces

In this paper, the authors study the boundedness of the operator [μΩ, b], the commutator generated by a function b ∈ Lipβ(Rn)(0 ＜β≤ 1) and the Marcinkiewicz integrals μΩ, on the classical Hardy spaces and the Herz-type Hardy spaces in the case Ω∈ Lipα(Sn-1)(0 ＜α≤ 1).     

Jacobi polynomials used to invert the laplace transform

Given the Laplace transform F(s) of a function f(t), we develop a new algorithm to find an approximation to f(t) by the use of the classical Jacobi polynomials. The main contribution of our work is the development of a new and very effective method to determine the coefficients in the finite series expansion that approximation f(t) in terms of Jacobi polynomials. Some numerical examples are illustrated.     

Generalization of the interaction between Haar approximation and polynomial operators to higher order methods

In applications it is useful to compute the local average empirical statistics on u. A very simple relation exists when of a function f（u） of an input u from the local averages are given by a Haar approximation. The question is to know if it holds for higher order approximation methods. To do so, it is necessary to use approximate product operators defined over linear approximation spaces. These products are characterized by a Strang and Fix like condition. An explicit construction of these product operators is exhibited for piecewise polynomial functions, using Hermite interpolation. The averaging relation which holds for the Haar approximation is then recovered when the product is defined by a two point Hermite interpolation.