随机加权法

在讨论置信区间和估计误差的分布等问题时,Efron 提出了 Bootstrap 方法.为说明 Bootstrap 方法,我们用均值估计的误差分布的计算这个例子说明之.设 X_1,…,X_n～iidF,考虑均值μ_1∫xdF 的估计误差     

二值回归模型中自变量误差的处理

In this paper the binary regression model, in which the response Y is binary, i.e. Y takes the value 0 or 1 only, is considered. The conditional probability P{Y=1|X=x} is assumed to be of the form G(a₀+a₁x), where x is the measurement of the factor, a= (a₀,a₁)′ is the vector of the unknown parameter being estimated and G(a) = (1+e^a)^-1. The measurement x is assu-med to be contaminated when the value of x is out of certain limit. M-estimation is employed to estimate the unknown a of the model. In this paper, the consistent M-estimation is proved to be asymptotically normal and the optimal M-equation is obtained. Finally, a computation method is introduced to solve the M-equation and to get the optimal solution.     

条件中位数的最近邻估计的大偏差概率的指数率

本文讨论了条件中位数的最近邻估计的大偏差问题。首先,在相当广泛的条件下,证明了条件中位数作为 x∈R~d 的函数,对几乎所有的 x,其最近邻估计的大偏差概率具有指数率;其次,在 x 为一维变量的情况下,考虑了条件中位数和它的最近邻估计在一致逼近意义下的距离。本文指出,当条件分布对 x 弱连续时,这个距离的大偏差概率具有指数率。由于本文所得到的结果,最近邻估计这个非参数方法可望在实际领域中得到更广泛的应用。     

随机删失半参数回归模型中估计的渐近性质

设Y是表示生存时间并遵从下面半参数模型Y=Xβ+g(T)+ε的随机变量,(X,T)是取值于R×[0,1]上的随机变量,β是未知参数,g(·)是[0,1]上的未知回归函数,ε是随机误差。当Y因受某种随机干扰而被随机右删失时,就删失分布未知的情形分别定义了β与g(·)的估计^{^}β_n与^{^}g_n(·),在一定条件下证明了^{^}β_n的渐近正态性,并得到了^{^}g_n(·)的最优收敛速度。     

左截断右删失下核密度估计的L1距离的界

本文在左截断右删失数据下获得了概论密度的核估计的L1距离的一个上界．     

一般回归模型中的U统计量

本文考虑一般回归模型中回归系数的方向的估计问题。一般回归模型的定义中,应变量y在自变量x给定之下的分布只依赖于x之分量的线性组合。这个线性组合的系数向量β就是回归系数向量。一般回归模型是通常线性模型的推广。本文中,我们构造了一个U统计量作为β之方向的估计。在适当的光滑性条件下,本文证明了该U统计量作为β的方向的估计具有相合性与渐近正态性。     

THE EXPANSION FOR THE ERROR DISTRIBUTION OF SAMPLE MEDIAN AND ITS RANDOM WEIGHTING STATISTIC

In this paper,the expansion for the error distribution of the sample median is obtained.To mimic the error distribution of the sample median,random weighting statistic is introduced.It is proved in this paper that the precision of the approximation of the error distribution for sample medisn by random weighting method is of the order of o.     

ON THE CONSISTENCY OF CROSS-VALIDATION IN NONLINEAR WAVELET REGRESSION ESTIMATION

1IntroductionConsidernonparametricregressiollwherextli=;E[O,1],En1,.',Ejl1larei.d.d.errorswitl11llea11o,a11dgisanunkl1ownfunctiontobeestimated-Nouparametricregressionestil11ationaimstoesti111atetl1euukllow11regressionfunctiong(x).Tl1enolllinearwaveletesti111atorshavebeenintroducedalldstudiedbyDonoho(1995).DonohoandJohnstoue(1994,1995).Do11oho,Johnstolle-KerkyachariallandPicard(1995)andDelyollandJuditsky(l996).Tl1eseauthorshavedenlo11stratedthevirtuesofllonlineaxwaveletmetl1odsf1o1llthev…     

STRONG REPRESENTATIONS OF THE SURVIVAL FUNCTION ESTIMATOR ON INCREASING SETS FOR TRUNCATED AND CENSORED DATA

1991MRSubjectClassification62G05,62E201IntroductionandtheMainResultsInthisarticlewestudysllrvivaldatawhicharesubjecttobothlefttrull(:ationandrightcensoring(LTRC).Morespecifically,let(X,T,Y)denoterandomvariableswhereXisthevariableofinterest,calledthelifetimevariable,withunknowndistributionfullctioll(d.f.)F;Tistherandomlefttruncatiolltiliiewitharbitraryd.f.G,andYistherandorl.1rightcensoringtirliewitharbitraryd.f.H.ItisassumedthatX,T,Yarerxlutuallyindependent.Intheran相似文献   

图模型及其在统计建模中的应用

图模型是近年来兴起的一个新的统计研究方向,主要借助拓扑图的直观形式对多维概率分布进行统计推断和因果分析。本文对图模型的基本概念、原理、建模及应用进行了简单介绍。