污染数据回归分析中估计的强相合性

考虑简单回归模型（Ⅰ）yi＝α＋xiβ＋εi，i＝1，2，…，n，与半参数回归模型（Ⅱ）yi＝xiβ＋g（ti）－εi，i＝1，2，…，n，其中Eεi＝0，Eεi2＝σ12．假定y1，y2，…，yn受到另一独立同分布随机变量序列μ1，μ2，…，μn的污染，且仅能观察到污染数据，｛μi｝与｛yi｝独立．对文[1]，[2]中给出的α，β，g（·）及污染参数v的估计，本文在适当的条件下，证明了它们的强相合性．     

关于两类污染数据回归分析的参数估计

研究简单回归模型：ｙｊ＝ａ＋βｘｊ＋εｊ，ｊ＝１，２，…，ｎ，其中Ｅεｊ＝０，Ｅε＾２ｊ＝σ＾２ｊ；但ｙ１，ｙ２，…，ｙｎ受到另一独立同分布随机变量序列ｔ，ｔ２，…，ｔｎ两种不同方式的污染，ｔｊ与ｙｊ独立。本文给出了两种污染方式下的ａ、β和污染参数的估计。     

污染数据线性回归模型参数估计的两个问题

研究了简单回归模型中响应变量在某一时刻受到另一随机变量序列污染时,模型参数和污染系数的估计方法及其相合性与渐近正态性,并证明了第Ⅰ类污染数据回归模型在假定22σ=l221σ(其中21σ和22σ未知,l2已知)下,其参数的矩估计不存在.     

污染数据半参数回归模型估计的渐近正态性

考虑半参数回归模型：yi=xiβ g(ti) e1,i=1,2,…,n,其中Ee1=0,Ee^2/1=δ2/1>0．假定y1,y2,…,y0受到另一独立同分布随机变量序列μ1,μ2,…,μn的污染,{μi}与{y1}独立,且仅能观察到污染数据.[ι]对由污染数据作出的参数β的估计βn,证明了它的强相合性．而本则证明了它的渐近正态性．     

污染数据回归分析中参数的最小一乘估计

考虑简单回归模型：ｙｉ＝ｘ′ｉβ＋ｅｉ,ｉ＝１,…,ｎ。其中Ｅｅｉ＝０,Ｅｅ＾２ｉ＝σ＾２１。假设ｙ１,ｙ２,…,ｙｎ受到另一独立同分布随机变量序列μ１,μ,…,μｎ的污染,我们仅能观察到污染数据ｙ＾＊ｉ＝（１－ν）ｙｉ,ν为未知的污染参数。本文用污染数据给出了β的最小一乘估计,并证明了它的渐近正态性和相合性。     

纵向数据下部分线性EV模型的渐近性质

研究了纵向数据下部分线性EV函数关系模型.应用一般非参数权函数法和广义最小二乘法给出了未知参数β,误差方差σ2以及未知函数g(·)的估计.在一般的条件下,证明了β,σ2估计的渐近正态性,同时也给出了未知函数g(·)估计的收敛速度,其结果是独立数据情形下相应结果的推广.     

固定设计的时间序列半参数回归

考虑如下的半参数回归模型Yi=xTiβ+g(ti)+εi(0≤i≤n),其中{εi,0≤i≤n}和{εt,0≤t≤n}有相同的联合分布,{εt,-∞＜t＜∞}是具有零均值和有限方差σ2的严平稳α-混合时间序列.本文构造了上述模型中β,g(t)和σ2的局部多项式估计,在适当的条件下,得到了估计的渐近正态性和收敛速度.在一定的假设下,β的估计是自适应的,而且g(υ)(t)(g(t)的第υ阶导数)的估计的收敛速度是最优的.     

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．     

污染数据情形下线性指数分布参数的经验贝叶斯估计（英文）

本文研究污染数据情形下线性指数分布参数的经验贝叶斯估计问题.在平方损失函数下,导出参数的贝叶斯估计以及利用解卷积的核方法构造该参数的经验贝叶斯估计.在合适的条件下,得到基于超平滑误差分布类所提出的经验贝叶斯估计的一致收敛速度.     

一类纵向数据半参数模型中的强相合估计

本文考虑如下纵向数据半参数回归模型:y_(ij)=x′_(ij)β+g(x_(ij))+e_(ij).结合最小二乘法和非参数权函数估计方法得到模型中参数β,回归函数g(·)的估计,并在适当条件下证明了估计量的强相合性.     

Minimum Distance Estimation in AR(1)-processes

In this paper a new minimum distance estimator is defined in case that the residuals of an AR(1)-process are contaminated normally distributed. This estimator is asymtotically normally distributed and in most cases less biased than the least square estimator. Furthermore, a method is presented to numerically calculate the minimum distance estimator as a root of an implicit function.     

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In this paper, linear regression models with contaminated data are considered. Estimation methods for the regression parameters based on least absolute deviations (LAD) are proposed, and properties of consistency and asymptotic normality of the proposed method are proved under some regular conditions. Simulations are done to assess the properties of the method when sample size is small, and simulation results show that the methods works well.     

Local powers of two-sample and multi-sample rank tests for Lehmann's contaminated alternative

Summary Local powers of two- andk-sample rank tests under alternatives of contaminated distributions are investigated. It is shown that the rank tests based on normal scores and Wilcoxon scores are superior to thet-test or theF-test for many choices of alternatives of contaminated distributions and that the values of the asymptotic relative efficiency of the rank test based on Wilcoxon scores with respect to the normal scores are about one in all the investigated cases.     

The asymptotic power of rank tests under scale-al ternatives including contaminated distributions

Summary The alternative hypothesis of translated scale for the classical non-parametric hypothesis of equality of two distribution functions in the two-sample problem is extended to a scale-alternative including contamination. The asymptotic power of rank tests and the two-sampleF-test under contiguous sequences of the alternatives is derived and asymptotic relative efficiency of these rank tests with respect to theF-test is investigated. It is found that some of the rank tests have reasonably high asymptotic powers satisfied enough.     

Nonparametric inference on the difference of location parameters of correlated variables from fragmentary samples

Summary In this paper, two types of robust estimators and approximate confidence intervals for the difference of location parameters of correlated random variables are proposed and investigated when some observations are missing. It is shown that the suggested estimators are consistent and asymptotically normally distributed. In addition, the proposed approximate confidence intervals are also shown to enjoy some nice asymptotic properties.     

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.     

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