部分线性模型的随机约束岭估计

研究了部分线性回归模型附加有随机约束条件时的估计问题.基于Profile最小二乘方法和混合估计方法提出了参数分量随机约束下的Profile混合估计,并研究了其性质.为了克服共线性问题,构造了参数分量的Profile混合岭估计,并给出了估计量的偏和方差.     

混合系数线性模型参数的广义Liu估计

本文研究连续测量数据情况下的混合系数线性模型的参数估计问题.利用压缩估计方法给出了该模型的一类新的有偏估计-广义Liu估计,并在均方误差意义下,证明此类估计分别优于最小二乘估计、Liu估计.最后讨论参数的选取问题.     

基于泛岭估计对岭估计过度压缩的改进方法

岭估计是解决多元线性回归多重共线性问题的有效方法,是有偏的压缩估计。与普通最小二乘估计相比,岭估计可以降低参数估计的均方误差,但是却增大残差平方和,拟合效果变差。本文提出一种基于泛岭估计对岭估计过度压缩的改进方法,可以改进岭估计的拟合效果,减小岭估计残差平方和的增加幅度。     

多元协方差阵扰动模型岭估计的影响分析

本文研究了多元线性同归模型岭估计的影响分析问题.利用最小二乘估计方法,获得了多元协方差阵扰动模型与原模型参数阵之间的岭估计的一些关系式,给出了度量影响大小的基于岭估计的广义Cook距离.     

惩罚的偏最小二乘

本文研究了二个推广的惩罚的偏小二乘模型,将惩罚估计的算法作用于偏最小二乘估计上,得到了参数的最终估计.将此模型运用到一个实际数据,在预测方面获得了较好的结果.     

多元线性模型回归系数的有偏估计与均方误差的无偏估计

本文对多元线性模型回归系数的最小二乘估计的任一线性变换，给出了均方误差的一个无偏估计，并应用统一方法，即极小化均方误差的无偏估计的方法，对岭估计和广义岭估计给出了确定偏参数的公式。最后给出了一个实例。     

部分线性变系数模型的随机约束岭估计

作为变系数模型和部分线性模型的推广,部分线性变系数模型近年来得到越来越多的关注.本文考虑该模型在线性部分自变量存在多重共线性并且参数分量附加有随机约束条件时的估计问题.基于profile最小二乘技术以及岭估计和混合估计方法,构造参数分量的profile混合岭估计,并且研究所提估计量的渐近性质.最后利用数值模拟验证所提估计方法的有效性.     

聚集数据线性模型参数的聚集综合岭估计的相对效率

对于聚集数据的线性模型,给出了参数的聚集综合岭估计的概念,并给出了聚集综合岭估计相对于最小二乘估计的两种相对效率,得到了这两种相对效率的上界.     

聚集数据线性模型参数的聚集改进综合岭估计的相对效率

对于聚集数据的线性模型,提出了参数的聚集改进综合岭估计的概念,并给出了聚集改进综合岭估计相对于最小二乘估计的两种相对效率,得到了这两种相对效率的上界.     

泛最小二乘法的改进及其容许性

考虑线性回归模型,当设计阵呈病态或秩亏时,我们用泛最小二乘法给出参数的估计,并证明其容许性;然后针对泛最小二乘估计对最小二乘估计过度压缩的缺点加以改进,使之更合理,有效.     

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.     

Instructions for Authors

<正>Submission Authors must use LaTeX for typewriting,and visit our website www.actamath.com to submit your paper.Our address is Editorial Office of Acta Mathematica Sinica,Academy of Mathematics and Systems Science,Chinese Academy of Sciences,Beijing 100190,P.R.China.     

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

正August 10-14,2015Beijin,China The 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     

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.     

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.     

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     

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     

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.