Making Use of Incomplete Observations for Regression in Bivariate Normal Model

Two estimates of the regression coefficient in bivariate normal distribution are considered: the usual one based on a sample and a new one making use of additional observations of one of the variables. They are compared with respect to variance. The same is done for two regression lines. The conclusion is that the additional observations are worth using only when the sample is very small.     

Constructing Solutions of an Ill-Posed Nonlinear Singularly Perturbed Problem for an Equation of Elliptic Type

Mathematical Notes -     

Theorems of Large Deviations in the Approximation by the Compound Poisson Distribution

The paper is devoted to the research of large deviation probabilities in the approximation by compound Poisson law.     

宁波市耕地动态及其驱动力的初步研究

利用宁波市55年长序列耕地统计数据,20余年相关社会经济资料,从宁渡市耕地的数量变化、利用程度的变化和变化的区域差异等方面,分析了宁波市耕地动态变化的趋势和规律．应用主成分分析,定量地诊断出耕地变化的驱动因子,揭示耕地变化的驱动机制．结果表明：耕地数量总体呈不断减少趋势,人口压力、经济发展动态是影响宁波市耕地动态变化的主要动因．在此基础上,运用多元回归分析建立耕地变化回归模型．该成果将为宁波市合理地利用和保护耕地提供理论指导．     

Information and asymptotic efficiency of the case-cohort sampling design in Cox's regression model

Efficiencies of the maximum pseudolikelihood estimator and a number of related estimators for the case-cohort sampling design in the proportional hazards regression model are studied. The asymptotic information and lower bound for estimating the parametric regression parameter are calculated based on the effective score, which is obtained by determining the component of the parametric score orthogonal to the space generated by the infinite-dimensional nuisance parameter. The asymptotic distributions of the maximum pseudolikelihood and related estimators in an i.i.d. setting show that these estimators do not achieve the computed asymptotic lower bound. Simple guidelines are provided to determine in which instances such estimators are close enough to efficient for practical purposes.     

Local polynomial fitting under association

We consider the estimation of multivariate regression functions r(x₁,…,x_d) and their partial derivatives up to a total order p1 using high-order local polynomial fitting. The processes {Y_i,X_i} are assumed to be (jointly) associated. Joint asymptotic normality is established for the estimates of the regression function r and all its partial derivatives up to the total order p. Expressions for the bias and variance/covariance matrix (of the asymptotic distribution) are given.     

Boltzmann-Poisson方程组初边值问题的整体弱解

§ 1.　Introduction　　LetΩ R3beasmoothboundedopenset,f(t,x ,v)bethedistributionfunctionofcar riersattimet >0 ,positionvectorx∈Ωandvelocityvectorv∈R3.Theforcefieldactingonthecarriersisdenotedbythe3 dimensionalvectorfunctionE(t,x) ,thepotentialcorespondingtoE(t,x)isdenotedbyu(t,x) ,then (f,E)satisfythefollowingBoltzmann Poissonsystem tf +v· xf +E· vf =Q(f) ,　 (t,x ,v)∈R+ ×Ω×R3,(1 .1 )E =- xu ,-Δxu =ρ ,　 (t,x) ∈R+ ×Ω ,(1 .2 )whereρ(t,x) =∫R3 f(t,x ,v)dvisthecarriernum…     

群胚上的Dirac结构及泊松约化

本文详细讨论了李双代数胚中的Dirac结构、群胚上的Dirac结构。利用Dirac结构的特征对的概念,给出了作用不变Dirac结构,拉回Dirac结构等概念的新的刻画。最后利用Dirac结构的有关性质,讨论了泊松齐性空间和泊松群胚作用的约化。     

在非线性回归模型中误差为AR(2)的相关性检验

本文讨论了在非线性回归模型中误差为AR(2)的相关性检验，得到了误差相关性检验的似然比检验统计量、Score检验统计量．对感兴趣参数和多余参数，利用Cox and Reid(1987)提出的正交化方法，给出了修正的似然比检验统计量和Score检验统计量．推广了胡跃清，韦博成(1994)讨论的在非线性回归模型中误差为AR(1)相关性检验的结果．     

半参数回归模型中小波估计的随机加权逼近速度

把小波光滑方法和随机加权方法结合在一起，获得了半参数回归模型中参数分量的小波估计的随机加权逼近速度为σ(n^-1/2)。因此，从大样本意义上说，小波光滑方法和随机加权方法对半参数回归模型是可用的。