约束条件下增长曲线模型中回归系数线性估计的泛可容许性

该文讨论了增长曲线模型$Y=X_{1}BX_{2}+\epsilon$在约束条件$X_{2}'B'X_{1}'NX_{1}BX_{2}\leq\Sigma$下回归系数线性估计$DYF$的泛可容许性问题,在损失函数$(d(Y)-KBL)'(d(Y)-KBL)$下,给出了回归系数的线性估计是泛可容许性的充要条件,其结果推广了文献中已有的结论.     

平衡损失下约束线性回归模型中回归系数的可容许估计

本文在平衡损失函数下得到等式约束模型中回归系数在齐次(非齐次)估计类中存在可容许估计的充要条件,给出带有不完全椭球约束模型中回归系数的线性估计在一切估计类中为可容许估计的充要条件.     

一般增长曲线模型回归系数线性估计的可容许性

在矩阵损失函数下,讨论了一般增长曲线模型中回归系数线性估计的可容许性问题,分别在齐次与非齐次估计类中给出了回归系数的线性估计是可容许估计的充要条件,推广了以往文献的相关结论.     

回归系数的非齐次线性估计的可容许性

考虑线性模型丁“Y一召…月二‘L刀Y一u”V,V>o,O’“为简便计,记为之Y,了月,砂V,V>0).若召是:x,阵,伺题.未知当习月可估时, (1)我们研究估计尽月的 RaoL刀给出了,在二次型损失函数 (‘一习月丫(d一习月)(2)下,S月的齐次线性估计L了在齐次线性估计类中是可容许估计的充要条件.本文考虑月月的非齐次线性估计L了+a的可容许性.在二次型损失函数下得到了LY十a在非齐次线性估计类中是习月的可容许估计的充要条件. 称R(S月,。,,d、~E(‘一习月)‘(d一召月)为习月的估计d的风险.若d,,d。是S尽的两个估计,当R〔泞月,。,,J,)一R(习月,a,,d:…     

二次损失下随机回归系数和参数的线性估计是可容许的充要条件

本文对于一般的随机效应线性模型(包括混合效应线性模型),在二次损失函数下给出了随机回归系数和参数的线性可估函数的齐次线性估计(线性估计)在齐次线性估计类(线性估计类)中可容许的充分必要条件.     

平衡损失下不等式约束回归系数的线性容许估计

对回归系数在不等式约束和平衡损失下讨论了其线性估计的可容许性,给出了齐次和非齐次线性估计类中可容许估计的充要条件.     

带约束一般生长曲线模型中可容许线性估计的特征

本文讨论带约束一般生长曲线模型中的可容许线性估计问题,对于回归系数的线性可估函数KBL的估计DYF(DYF+M),分别在齐次和非齐次线性估计类中,给出了它们是可容许估计的一些特征.     

带约束的回归系数的线性估计的可容许性

在本文中,我们针对带齐次线性等式约束的线性模型Y=Xβ+ε,ε～(0,σ~2V),Hβ=0,给出了回归系数的最佳线性无偏估计的较简单的表达式以及Sβ的估计LY(LY+α)在齐次线性估计类(线性估计类)中可容许的充要条件。     

矩阵损失函数下回归系数矩阵的非齐次线性估计的可容许性

在二次矩阵损失函数下研究了协方差矩阵未知的多元线性模型中回归系数矩阵的可估线性函数的矩阵非齐次线性估计的可容许性,给出了矩阵非齐次线性估计在线性估计类中可容许的一个充要条件.     

带有不完全椭球约束的生长曲线模型中线性估计的可容许性

对于带有不完全椭球约束的生长曲线模型Y=XBZ+ε,ε~(0,σ2VI),X(B-B0)Z′NZ(B-B0)′X′≤σ2In,本文在矩阵损失函数(d-KBL)(d-KBL)′下给出了KBL在类齐次线性估计类LH与非齐次线性估计类LI中可容许的充要条件.本文的结果表明线性估计在非齐次线性估计类中的可容许性与椭球的中心B0无关,而齐次线性估计在齐次线性估计类中的可容许性与B0有关.     

带有不等式约束的生长曲线模型中回归系数线性估计的泛容许性

对于带有不等式约束的生长曲线模型：Y=XBZ＋ε，ε^→～（0，σ^2V×I），tr（NB）≥0，本文在矩阵损失函数（d—KBL）（d—KBL）＇下，给出了可估函数KBL的线性估计的泛（西）容许性定义，分别得到了DYF和DYF＋C在齐次估计类LH和非齐次估计类LI中是KBL的泛容许性估计的充要条件．     

矩阵损失下随机回归系数和参数的线性Minimax估计

对于一般的随机效应线性模型Y=Xβ+ε,这里β和ε分别是p维和n维的随机向量,且E(βε)=(Aa0),Cov(βε)=σ2(V10 0V2),(Vi≥0,i=1,2)我们定义了Sα+Qβ的线性Minimax估计,在一定条件下得到了Sα+Qβ在线性估计类中的Minimax估计,并在几乎处处意义下证明了它的唯一性.     

ASYMPTOTIC NORMALITY OF THE NONPARAMETRIC KERNEL ESTIMATION OF THE CONDITIONAL HAZARD FUNCTION FOR LEFT-TRUNCATED AND DEPENDENT DATA

Under some mild conditions, we derive the asymptotic normality of the Nadaraya-Watson and local linear estimators of the conditional hazard function for left-truncated and dependent data. The estimators were proposed by Liang and Ould-Sa?d [1]. The results confirm the guess in Liang and Ould-Sa?d [1].     

An extended class of minimax generalized Bayes estimators of regression coefficients

We derive minimax generalized Bayes estimators of regression coefficients in the general linear model with spherically symmetric errors under invariant quadratic loss for the case of unknown scale. The class of estimators generalizes the class considered in Maruyama and Strawderman [Y. Maruyama, W.E. Strawderman, A new class of generalized Bayes minimax ridge regression estimators, Ann. Statist., 33 (2005) 1753–1770] to include non-monotone shrinkage functions.     

Consistency and asymptotic normality of profilekernel and backfitting estimators in semiparametric reproductive dispersion nonlinear models

Semiparametric reproductive dispersion nonlinear model (SRDNM) is an extension of nonlinear reproductive dispersion models and semiparametric nonlinear regression models, and includes semiparametric nonlinear model and semiparametric generalized linear model as its special cases. Based on the local kernel estimate of nonparametric component, profile-kernel and backfitting estimators of parameters of interest are proposed in SRDNM, and theoretical comparison of both estimators is also investigated in this paper. Under some regularity conditions, strong consistency and asymptotic normality of two estimators are proved. It is shown that the backfitting method produces a larger asymptotic variance than that for the profile-kernel method. A simulation study and a real example are used to illustrate the proposed methodologies. This work was supported by National Natural Science Foundation of China (Grant Nos. 10561008, 10761011), Natural Science Foundation of Department of Education of Zhejiang Province (Grant No. Y200805073), PhD Special Scientific Research Foundation of Chinese University (Grant No. 20060673002) and Program for New Century Excellent Talents in University (Grant No. NCET-07-0737)     

方差分量线性模型中回归系数和参数的所有可容许线性估计

对固定效应方差分量模型，在矩阵损失（ｄ－Ｓ＿τ）（ｄ－Ｓ＿τ）＇下，我们给出了线性可估函数Ｓτ的线性估计在一切估计类中可容许的充要条件；对具有两个方差分量的随机效应线性模型在矩阵损失（ｄ－Ｓα－Ｑβ）（ｄ－Ｓα－Ｑβ）＇下，我们给出了线性可估函数Ｓα＋Ｑβ的线性估计在一切估计类中可容许的充要条件。     

Linear plus quadratic (LPQ) quasiminimax estimation in the linear regression model

If the errors in the linear regression model are assumed to be independent with nonvanishing third and finite fourth moments, then it is possible to improve all linear estimators by so-called linear plus quadratic (LPQ) estimators. These consist of linear and quadratic terms in the endogeneous variable and depend on the unknown moments of the errors which, in general, have to be estimated from the data. In this paper, we will use LPQ estimators for quasiminimax estimation and some related problems.Support by Deutsche Forschungsgemeinschaft Grant No. Tr 253/1-2 is gratefully acknowledged.     

A posteriori estimators for nonlinear elliptic partial differential equations

Many works have reported results concerning the mathematical analysis of the performance of a posteriori error estimators for the approximation error of finite element discrete solutions to linear elliptic partial differential equations. For each estimator there is a set of restrictions defined in such a way that the analysis of its performance is made possible. Usually, the available estimators may be classified into two types, i.e., the implicit estimators (based on the solution of a local problem) and the explicit estimators (based on some suitable norm of the residual in a dual space). Regarding the performance, an estimator is called asymptotically exact if it is a higher-order perturbation of a norm of the exact error. Nowadays, one may say that there is a larger understanding about the behavior of estimators for linear problems than for nonlinear problems. The situation is even worse when the nonlinearities involve the highest derivatives occurring in the PDE being considered (strongly nonlinear PDEs). In this work we establish conditions under which those estimators, originally developed for linear problems, may be used for strongly nonlinear problems, and how that could be done. We also show that, under some suitable hypothesis, the estimators will be asymptotically exact, whenever they are asymptotically exact for linear problems. Those results allow anyone to use the knowledge about estimators developed for linear problems in order to build new reliable and robust estimators for nonlinear problems.     

Nonparametric density estimation for linear processes with infinite variance

We consider nonparametric estimation of marginal density functions of linear processes by using kernel density estimators. We assume that the innovation processes are i.i.d. and have infinite-variance. We present the asymptotic distributions of the kernel density estimators with the order of bandwidths fixed as h =  cn ^−1/5, where n is the sample size. The asymptotic distributions depend on both the coefficients of linear processes and the tail behavior of the innovations. In some cases, the kernel estimators have the same asymptotic distributions as for i.i.d. observations. In other cases, the normalized kernel density estimators converge in distribution to stable distributions. A simulation study is also carried out to examine small sample properties.     

一种改进的半参数极大似然法估计量的渐近性质

本文研究线性回归模型, Y=β'X+∈,并假设Y可被右删失,∈的分布函 数F0未知.本文证明,在某些条件下, β的一种改进的半参数极大似然法估计量β 有相合性. 同时证明,如果F0不连续,则P{β≠βi.o.}=0.这意味着以概率为一, 当样本很大时, β=β.文献中的现有估计量未见有关于这一性质的报道.相反,包括 Buckley-James估计量及M-估计量在内的大多数的估计量,都不满足这一性质.