增长曲线模型的参数估计及其性质

考虑增长曲线模型：Ｙｐ×ｎ＝ＡＢＣ＇＋εｐ×ｎ，Ｅε＝０．其中，ε＝（ε１，ε２，…，εｎ），ε１，ε２…，εｎ独立同分布，Ｅεｉεｉ＇＝Σｐ×ｐ＞０．该文利用协差阵的Σ的（一定意义下的）最小二乘估计Σ，分别给出了参数Ｂ，参数的线性函数ＡＢ，ｔｒ（Ｄ１’Ｂ）＋（Ｄ２Σ）（Ｄ２＝Ｄ‘２）（Ｄ２＝Ｄ２’）的估计Ｂｎ，Ｚｎ和ｔｒ（Ｄ１＇Ｂｎ）＋ｔｒ（Ｄ２Σｎ）．在ε１服从正态分布的情形下，给出了Ｚｎ，Σｎ的分布．并在ε１分布比较一般的情形和一定条件下给出了Ｚｎ，Ｂｎ，Σｎ和ｔｒ（Ｄ１’Ｂｎ）＋ｔｒ（Ｄ２Σｎ）的极限分布皆为正态分布（ｎ→∞）．而且Ｚｎ，和Σｎ，Ｂｎ，和Σｎ都是渐近独立的（ｎ→∞）．从而可构造参数Ｂ的置信区域和更好地进行判别分析，相关分析等．     

多元线性模型中的一个参数函数的UMVIQUE的存在性

考虑多元线性模型 Y=X_1BX＇_2 Uε,Eε=0,其中ε=（ε_1,…,ε_n）＇,ε==(ε_1',...ε_n'),E(εε)=I（×）∑,∑≥0。是未知协差阵。本文给出了tr（C∑）的一致最小方差不变二次无偏估计（简记为UMVIQUE）存在的充要条件。     

一般增长曲线模型回归系数线性估计的可容许性

一般增长曲线模型回归系数线性估计的可容许性孙六全（华中师范大学数学系，武汉４３００７０）§１引言本文考虑一般的增长曲线模型其中Ｙ，ε为ｍ×ｎ阶随机矩阵，Ａｍ×ｐ，Ｂｋ×ｎ为已知的常数矩阵，矩阵及σ２＞０是未知参数，ｍ×ｍ阶矩阵已知，ε表示ε按列拉直。...     

Moderate deviations and central limit theorem for small perturbation Wishart processes

Let X^ε be a small perturbation Wishart process with values in the set of positive definite matrices of size m, i.e., the process X^ε is the solution of stochastic differential equation with non-Lipschitz diffusion coefficient： dXt^ε = √εXt^εtdBt＇ ＋ dBt＇√εXt^ε ＋ ρImdt, X0 = x, where B is an rn x m matrix valued Brownian motion and B＇ denotes the transpose of the matrix B. In this paper, we prove that { （Xt^ε-Xt^0）/√εh^2（ε）,ε 〉 0} satisfies a large deviation principle, and （Xt^ε - Xt^0）/√ε converges to a Gaussian process, where h（ε） → ＋∞ and √ε h（ε） →0 as ε →0. A moderate deviation principle and a functional central limit theorem for the eigenvalue process of X^ε are also obtained by the delta method.     

生长曲线模型中二次估计的非负最优性

考虑生长曲线模型Ｙ＝Ｘ１ＢＸ２＇＋ε，Ｅε＝０。设ε＝（εβ．．．εｎ）＇，ε＝（ε＇．．．εｎ＇）＇．Ｅεε＇＝Ｉ为未知协差阵，本文讨论了ｔｒ（ＣΣ）（Ｃ＜０）的一致最小方差非负二次无偏估计（简称为最优非负估计）问题，给出了一般二次估计是ｔｒ的最优非负估计的充要条件，从而得到ｔｒ的最优非负估计存在的充要条件，以及ｔｒ是ｔｒ的最优非负估计的充要条件。     

一个特殊除数问题

设△（x）为D＊（a,b;x）=∑manb≤x（m,n）=1 1（1≤a0,有△（x） 当b≤3a/2时;当b>3a/2时.     

一个半参数模型渐近有效估计的构造

对半参数回归模型Ｙ＝ＸＴβ十ｇ（Ｔ）＋ε，分别在ε的密度函数已知、未知的情况下，构造出了β的渐近有效估计．     

相依回归系统一种协方差改进估计之协方差阵的无偏估计

考虑相依回归方程系统ｙｉ＝Ｘｉβｉ＋εｉ（ｉ＝１，２），Ｅ（εｉ）＝０，Ｃｏｖ（εｉ，εｊ）＝σｉｊＩｎ。记βｉ为βｉ的协方差改进估计＾［１］。σｉｊ未知时，记βｉ为用非限定估计σｉｊ代替βｉ中的σｉｊ得到的两步估计，并记βｉ为用限定估计σｉｊ代替βｉ中的σｉｊ得到的两步估计，这两种两步估计的协方差中含有未知参数σｉｊ代替βｉ中的σｉｊ得到的两步估计，这两种两步估计的协方差中含有未知参数σｉｊ。本     

一般增长曲线模型参数阵的BLU估计

考虑一般增长曲线模型：Ｙ＝Ｘ１ＢＸ２＋εＥ（Ｖｅｃ（ε））＝０Ｖ（Ｖｅｃ（ε））＝σ２ＶＩｎ（Ｖ０）本文对任一可估函数ＫＢＬ给出了它的ＢＬＵ估计（最佳线性无偏估计），并得到了方差σ２的一个无偏估计．     

Gauss—Markoff估计的协方差改进形式及其在SUR模型中的应用

本文采用并推广Rao[1]的协方差改进原理，证明了线性模型（1．1）的Gauaa－Markoff估计（1．2）具有协方差改进形式＝（X′X）－1X′Y－（X′X）－1X′VN［NVN］＋NY，其中N＝I－X（X′X）－1X′．这一结果用于SUR系统yi＝Xiβi＋εi（i＝1，2，…，m），容易得到Zellner两步估计的有限样本性质．本文得到了一类系统的有限样本方差结果，从而完善了一些已有结果．     

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.