M-估计下误差密度核估计的相合性

线性模型Yi=x′iβ ei,i=1,2…，其中{ei}i^∞=1,i.i.d.,有未知密度f(x），本文讨论了在对β作一般M－估计后，基于残差做出的误差密度核估计的相合性，在比文献弱的条件下，证明了误差密度核估计的逐点弱相合，逐点强相合和一致强相合。     

基于M—估计的误差密度估计

对于线性模型 Yi=x＇_iβ十e_i,i=1,2,...,{e_i}_(i= 1)~∞i.i.d.,e_1有未知密度函数f（x）,本文基于β的M-估计的残差:e_i=Yi—x＇_iβ,i=1,2,…,n,其中β为β的M-估计,用 f_n(x)=1/2na_n sum from i=1 to n I(x-a_ne_i^≤x a_n)估计f(x）,得到了这种估计的强收敛速度,一致强收敛速度,L_1-模相合性,渐近正态性,重对数律。     

误差为MA（∞）序列的半参数回归模型的小波估计的渐近性质

本文研究误差为MA(∞)时间序列的半参数回归模型.利用小波方法,研究了参数分量β非参数分量g(t)的小波估计βn、gn(·)的渐近性质.在适当的条件下,得到了βn的渐近正态性、强收敛速度、矩收敛速度及gn(·)的强相合性和矩相合性.     

基于网点观测的变量不全含误差的部分线性函数关系模型

对一类基于网点观测的部分线性变量含误差模型进行了研究,解释变量为(xτ,μτ,t)τ,其中x带有观测误差,而μ,t不含误差为真实值,文中用最小二乘原理给出了未知参数的估计,并利用一阶样条方法给出了未知函数的估计．在较弱的条件下证明了估计量的强相合性。给出了a．s．收敛速度．     

相依样本下线性模型误差分布的相合估计

对于线性模型狔犻＝狓犻′β＋犲犻，犻＝１，…，狀，设误差序列｛犲犻｝是平稳的α 混合序列，犳（狓）为其 公共的未知密度函数，我们讨论了基于残差的犳（狓）的核估计＾犳狀（狓）＝１狀犪狀∑狀犻＝１犓（＾犲狀犻－狓犪狀）的弱相合性、逐点强相合性、一致强相合性及其收敛速度，其中＾犲狀犻为Ｌ．Ｓ．估计的残差．     

对称的稳定分布参数变点估计的相合性

假设稳定分布的特征指数α满足1<α<2,关于均值μ对称. 本文讨论了稳定分布中α或刻度参数β的变化导致的变点问题,即是否发生变化及变化时刻.若均值已知,当α或β改变时,密度函数f(x)在μ处的值f(μ)发生变化,我们利用密度函数的核估计来估计该点的值. 若均值未知,利用经验特征函数估计该点的值,并进一步讨论了估计的相合性与收敛速度. 其次讨论了均值变化导致的变点问题,若均值发生变化,相应变点前后特征函数的参数将变化,利用经验特征函数给出了变点的估计, 获得了类似的收敛速度. 最后给出了检测金融市场突变性的应用.     

基于网点观测的变量不全含误差的部分线性函数关系模型

对一类基于网点观测的部分线性变量含误差模型进行了研究,解释变量为(xτ,μτ,t)τ,其中x带有观测误差,而μ,t不含误差为真实值,文中用最小二乘原理给出了未知参数的估计,并利用一阶样条方法给出了未知函数的估计.在较弱的条件下证明了估计量的强相合性,给出了a.s.收敛速度.     

相依样本非参数回归模型误差的相合估计

考虑非参数回归模型Y_i=g(X_i) c_i,i=1,2,…,其中误差㈦)为吵混合随机变量序列且具有公共的未知密度f(·),g(x)=E(Y|X=t)为未知回归函数。本文首先基于g(·)的非参数估计l(x)定义残差,然后基于残差构造f(·)的估计l(x),最后在适当条件下建立l(x)的逐点相合性及一致强相合性。     

相依样本下一种近邻密度估计的相合性

设{ Xn}^∞ n=1是R^1中的平稳过程,具有公共的未知密度函数f(x) ,我们研究基于前n个观测值X1,X2,… Xn的f(x)的一种近邻估计fn(x).本文假定{Xn}^∞ n=1O φ-混合或强混合的,在对混合系数φ(n)趋于零的速度的适当限制下,证明了fn(x)的逐点相合性一致强相合性.并得到了这两种相合性强收敛速度.     

ρ—混合序列加权和的完全收敛性

对混合速度不作限制下，讨论了ρ－混合序列加权和Ｔｎ＝Σ（ｎ，ｋ＝１）αｎｋＸｋ的完全收敛性，推广了Ｗ．Ｆ．Ｓｔｏｕｒｔ的结果。将此新结果应用于线性模型参数β的估计中，得出β的最小二乘估计βｎ的强相合性     

A REPRESENTATION FORMULA RELATED TO SCHR(O)DINGER OPERATORS

Schr(o)dinger operator is a central subject in the mathematical study of quantum mechanics.Consider the Schrodinger operator H = -△ V on R, where △ = d2/dx2 and the potential function V is real valued. In Fourier analysis, it is well-known that a square integrable function admits an expansion with exponentials as eigenfunctions of -△. A natural conjecture is that an L2 function admits a similar expansion in terms of "eigenfunctions" of H, a perturbation of the Laplacian (see [7], Ch. Ⅺ and the notes), under certain condition on V.     

On a class of self-similar processes with stationary increments in higher order Wiener chaoses

We study a class of self-similar processes with stationary increments belonging to higher order Wiener chaoses which are similar to Hermite processes. We obtain an almost sure wavelet-like expansion of these processes. This allows us to compute the pointwise and local Hölder regularity of sample paths and to analyse their behaviour at infinity. We also provide some results on the Hausdorff dimension of the range and graphs of multidimensional anisotropic self-similar processes with stationary increments defined by multiple Wiener–Itô integrals.     

On a class of Riemann surfaces

It is considered the class of Riemann surfaces with dimT1 = 0, where T1 is a subclass of exact harmonic forms which is one of the factors in the orthogonal decomposition of the spaceΩH of harmonic forms of the surface, namely The surfaces in the class OHD and the class of planar surfaces satisfy dimT1 = 0. A.Pfluger posed the question whether there might exist other surfaces outside those two classes. Here it is shown that in the case of finite genus g, we should look for a surface S with dimT1 = 0 among the surfaces of the form Sg\K , where Sg is a closed surface of genus g and K a compact set of positive harmonic measure with perfect components and very irregular boundary.     

CONTENTS OF VOLUME 30

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Instructions for contributions

正Applied Mathematics-A Journal of Chinese Universities,Series B(Appl.Math.J.Chinese Univ.,Ser.B)is a comprehensive applied mathematics journal jointly sponsored by Zhejiang University,China Society for Industrial and Applied Mathematics,and Springer-Verlag.It is a quarterly journal with     

Journal of Mathematical Research with Applications Guide for Authors

正Journal overview:Journal of Mathematical Research with Applications(JMRA),formerly Journal of Mathematical Research and Exposition(JMRE)created in 1981,one of the transactions of China Society for Industrial and Applied Mathematics,is a home for original research papers of the highest quality in all areas of mathematics with applications.The target audience comprises:pure and applied mathematicians,graduate students in broad fields of sciences and technology,scientists and engineers interested in mathematics.     

Staircase transportation problems with superadditive rewards and cumulative capacities

A cumulative-capacitated transportation problem is studied. The supply nodes and demand nodes are each chains. Shipments from a supply node to a demand node are possible only if the pair lies in a sublattice, or equivalently, in a staircase disjoint union of rectangles, of the product of the two chains. There are (lattice) superadditive upper bounds on the cumulative flows in all leading subrectangles of each rectangle. It is shown that there is a greatest cumulative flow formed by the natural generalization of the South-West Corner Rule that respects cumulative-flow capacities; it has maximum reward when the rewards are (lattice) superadditive; it is integer if the supplies, demands and capacities are integer; and it can be calculated myopically in linear time. The result is specialized to earlier work of Hoeffding (1940), Fréchet (1951), Lorentz (1953), Hoffman (1963) and Barnes and Hoffman (1985). Applications are given to extreme constrained bivariate distributions, optimal distribution with limited one-way product substitution and, generalizing results of Derman and Klein (1958), optimal sales with age-dependent rewards and capacities.To our friend, Philip Wolfe, with admiration and affection, on the occasion of his 65th birthday.Research was supported respectively by the IBM T.J. Watson and IBM Almaden Research Centers and is a minor revision of the IBM Research Report [6].