固定设计下一类半参数回归模型的渐近性质

对固定设计下的一类半参数回归模型yi=xiβ+g(xi)+ei,i=1,2,…,n,综合最小二乘和非参数权函数估计方法,定义了,βg的估计量β∧n,gn∧及误差方差σ2的估计量σ2n∧.在适当条件下,证明它们具有强相合性和p(2)阶平均相合性.模拟的结果表明所得结果具有优良的性质.     

混合误差半参数回归模型估计的强相合性

对半参数模型y（n）i＝β（n）xi＋g（t（n）i）＋ε（n）i，i＝1，2，…，n，综合运用最小二来法和非参数估计法，定义了β，g的估计量　，gn，在误差为某些混合序列下，得到了，gn（t）的强相合性及gn（t）的一致强相合性．     

PA误差下半参数回归模型小波估计的r-阶矩相合性

对于半参数回归模型y_i=x_iβ+g(t_i)十e_i,(1≤i≤n),其中{e_i,1≤i≤n}为PA相依误差.在适当的条件下,利用极大部分和的矩不等式方法得到未知回归函数g(x)和未知参数β估计量的r-阶矩相合性.     

PA误差下半参数回归模型小波估计的γ-阶矩相合性

对于半参数回归模型yi=xiβ+g(ti)+ei,(1≤i≤n),其中{ei,1≤i≤n}为PA相依误差.在适当的条件下,利用极大部分和的矩不等式方法得到未知回归函数g(x)和未知参数β估计量的r-阶矩相合性.     

误差为鞅差序列的半参数回归模型估计的相合性

设半参数回归摸型Y^(n)=β·χi(1) g(l1^(n)) 1 ^(n),i=1,2,…．n,本由最小二乘法和一般加权方法定义的β、g(t)的怙计量βn,gn(t)．在误差为鞅差序列下获得了βn gn(f)的r(≥2)阶平均相合性。     

相协样本半参数回归模型估计的强相合性

考虑半参数回归模型Y^(j)(xin,lin)=tinβ g(xin) e^(j)(xin)，1≤j≤m，1≤i≤n,利用最小二乘法和权函数估计方法，定义β，g的估计量βm,n和gm,n(x)，在负相依样本及较弱的条件下证明了这些估计的强相合性，得到了与独立情形一致的结论．     

误差为线性过程时半参数模型的估计

对半参数模型Ynt=β·tni＋g（xni）＋εni,（1≤i≤n）,利用一般权函数并综合最小二乘法,定义了β,g的估计量βn,gn．在误差为线性过程时,获得了βn和gn的r阶矩相合性及gn的渐进正态性．     

误差为NA序列的半参数回归模型估计的r阶矩相合性

对于半参数回归模型y1=xiβ＋g(ti) ei,i=1,2,…,n,本综合最小二乘法和一般加权方法,定义了β,g(t)的估计量βn,gn(t),在误差为NA序列进,得到了βn,gn(t)的r(r≥2)阶矩相合性。     

NA样本固定设计下半参数回归模型中估计的强相合性

对于半参数回归模型yi=xiβ g(ti) ei，i=1，2,…，n(xi，ti)为已知的固定设计点列．本在误差{e．1≤n≤n)为NA序列时，对g(t)和σ的估计量gn~(t)和σn^2的逐点强相合。以及gn~(t)的一致强相合作了研究，得到比较理想的结果。     

固定设计下的非参数多元回归

设Y(n)i=g(x^(n)i) ε^(n)i,g 为未知函数,x^(n) i为已知设计点列,ε^(n)i 为 随机误差.用gn(x)=∑^ni=1Wni (x,x1^(n),…,x^(n)nY^(n)i估计g(x),在误差为某些相依随机变量列时,我们获得了gn(x)的r阶平均相合和一致强相合性.     

异方差回归模型近邻型估计的相合性

本文研究异方差回归模型Ｙｉ＾（ｎ）＝ｇ（ｘｉ＾（ｎ））＋εｉ＾（ｎ）,ｉ＝１,…,ｎ,其中ｇ是右实函数,ｘｉ＾（ｎ）是非随机设计点列,εｉ＾（ｎ）是随机误差,文中定义了一类ｇ（ｘ）的近邻型估计ｇｎ（ｘ）＝（ｎ）∑（ｉ＝１）Ｗｍ（ｘ）Ｙｉ＾（ｎ）,得到了ｒ阶平均相全和渐近正态性,特别,在（∞）∑（ｎ＝１）（ｎ）∑（ｉ＝１）Ｅ／εｉ＾（ｎ）／＾ｓ／（ｎｉ）＾ｓ／ｒ〈∞,ｍａｘＥ（１≤ｉ≤ｎ）／εｉ（＾     

拟协调元的精度分析

利用双参数有限元的框架，证明利用拟协调元方法构造的非协调三角形板元都具有一个非常特殊的性质。即相容误差比插值误差高一阶。这是常规有限元和一般非协调元所不具备的。     

A NOTE ON THE CONSISTENCY OF LS ESTIMATES IN LINEAR MODELS

Consider,the linear regression modelyi = x'iβ ei, 1≤i≤n, n≥1, (1)where x1, x2,' are known Hvectors, P is the unknown pdimensional vector of regressioncoefficiellts, e13 e2,' is a seqdence of iid. random errors, and y1, y2t' are known obser-vations of the dependellt variable. Denote by F the common distribution of e1, e2,' t andwrite9. = {F: j:xar=0, 0< j:lxl'aF< oo}, 1 5 r 5 2.The Least Squares (LS) estimate of P isn rs)n = Z SJ'x.ui, Sn = Zxix:.. i=1 i=1Here we tacitly assum…     

SOME LARGE SAMPLE PROPERTIES OF AN ESTIMATOR OF THE HAZARD FUNCTION FROM RANDOMLY CENSORED DATA

1IntroductionInmaplifetimestudies,someOfthesubjects"liderstudyarecensoredontherightbyapriorcensoringtime.LetTI,T2,'',TibeindependentandidenticallydistributednonnegativerandomvariableswithcommoncontinuousdistributionfullctionFandcontinuousprobabilitydensityfunctionf.Inthemodelofrightrandomcensoring,associatedwitheachZthereisanindependentnonnegativecensringtimeCiandCI,C2,'',CdareassumedtobelidrandomvariableswithcontinuotisdistributionfunctiollG.Illthismodelwecanobserveonlythepairs(Xi,hi)…     

NA样本下半参数回归模型估计的强相合性

考虑固定设计下的半参数回归模型;yi=xiβ g(ti) ei,i=1,2……,n,在{ei}为Eei=0,Ee^2i=σ^2i的NA序列时,得到了一类估计的强相合性。     

CONVERGENCE ANALYSIS OF MORLEY ELEMENT ON ANISOTROPIC MESHES

The main aim of this paper is to study tile convergence of a nonconforming triangular plate element-Morley element under anisotropic meshes. By a novel approach, an explicit bound for the interpolation error is derived for arbitrary triangular meshes （which even need not satisfy the maximal angle condition and the coordinate system condition ）, the optimal consistency error is obtained for a family of anisotropically graded finite element meshes.     

独立误差下线性回归最小二乘估计相和性的必要条件

对线性回归Yi=x'iβ+ei,i=1,…,n,…,其中x1,x2,…为已知P维向量,e1,e2,…为随机误差.本文证明了:如果e1,e2,…独立,每一个非退化,则是β的最小二乘估计相合的必要条件,注意此处对ei的期望和方差没有施加任何条件.     

截尾变量独立,不必同分布的条件下,最大似然估计的相合性及渐近正态性

本文提出条件（φ）,并证明了,在条件（φ）下,关于寿命分布的参数的最大似然估计具有强相合性及渐近正态性。验证了指数分布、Weibull分布、对数正态分布满足条件（φ）。这说明（φ）是比较广泛适用的。     

ON THE ANISOTROPIC ACCURACY ANALYSIS OF ACMES NONCONFORMING FINITE ELEMENT

The main aim of this paper is to study the superconvergence accuracy analysis of the famous ACM＇s nonconforming finite element for biharmonic equation under anisotropic meshes. By using some novel approaches and techniques, the optimal anisotropic interpolation error and consistency error estimates are obtained. The global error is of order O（h^2）. Lastly, some numerical tests are presented to verify the theoretical analysis.     

The consistency index in reciprocal matrices: Comparison of deterministic and statistical approaches

When checking the inconsistency level of a positive reciprocal matrix Saaty uses a deterministic criterion based on two parameters, a benchmark (the average), and a consistency level, usually 10%. Using results from a simulation experiment with 100,000 positive random reciprocal matrices of size varying from 3 to 15, we developed a probabilistic criterion and compare it to Saaty’s index. We found that if a positive reciprocal matrix is consistent according to the deterministic criterion is also consistent according to the probabilistic criterion only if we accept a higher than usual probability of Type I error. Reducing this error implies that the benchmark must be a small percentile of the probability distribution of the consistency index.