自然联系函数下自适应设计广义线性模型的渐近性质(英文)

本文在一些弱的条件下,对自然联系函数和自适应设计下广义线性模型的极大拟似然估计渐近性进行研究,获得了极大拟似然估计的渐近存在性、弱相合性、收敛速度及渐近正态性.并通过蒙特卡罗数值模拟的方法对所得结果进行验证.     

强相依数据的函数系数部分线性模型的估计

本文讨论在数据是强相依的情况下函数系数部分线性模型的估计．首先,采用局部线性方法,给出该模型函数项函数的估计;然后,使用两阶段方法给出系数函数的估计．并且讨论了函数项函数估计的渐近正态性,以及系数函数估计的弱相合性和渐近正态性.模拟研究显示,这些估计是较为理想的．     

半参数混合效应模型中的估计及其强相合性

将Tao等(1999)提出的线性混合效应模型推广为半参数混合效应模型,给出了模型参数、回归函数和随机效应密度的估计,并研究了估计的强相合性及部分强相合速度.统计模拟表明我们给出的估计方法是可行的.     

一种估计Clayton模型中关联参数的方法

在右删失情形下,基于二元风险函数的核估计,我们对Clayton模型中的关联参数给出了一种新的估计方法.新的估计量具有相合性和渐近分布,随机模拟也显示这种估计方法是非常有效的.     

基于变系数模型的纵向数据相关结构选择和估计

本文针对基于变系数模型的纵向数据提出 选择和估计其个体内部相关结构的方法, 给出变系数模型中系数函数曲线的有效估计, 并建立相应的大样本渐近性质. 模拟结果和实例分析表明, 即使在有限样本下, 本文所提方法在选择和估计真实相关结构方面具有相合性, 并能够提高系数函数曲线的估计效率.     

固定设计下半参函数关系模型参数估计的相合性

对于固定设计下的半参数函数关系模型,利用广义最小二乘法和一般的非参数权估计方法,得出了未知参数和未知函数的估计.在一定条件下,证明了它们的强相合性及其p(≥2)阶平均相合性.     

纵向数据下非参数带测量误差的部分线性变系数模型的估计

本文研究纵向数据下非参数部分带有测量误差的部分线性变系数模型的估计.利用B样条函数近似模型中的变系数函数,构造偏差修正的二次推断函数,得到模型中未知参数和变系数函数的估计.证明变系数函数估计量的相合性和参数估计量的渐近正态性.数值模拟和实例分析结果表明所提估计方法在有限样本下的有效性.     

左截断相依数据下非参数回归的局部M 估计

本文对左截断模型, 利用局部多项式的方法构造了非参数回归函数的局部M 估计. 在观察样本为平稳α-混合序列下, 建立了该估计量的强弱相合性以及渐近正态性. 模拟研究显示回归函数的局部M 估计比Nadaraya-Watson 型估计和局部多项式估计更稳健.     

带自回归过程的单指标模型的参数估计及其渐近性质

研究了带有一阶自回归误差结构的单指标模型的参数估计及其渐近性质问题,利用局部多项式回归的方法对未知的联系函数进行估计,基于最大似然方法提出了模型的参数估计方法,同时在一些基本的假设下证明了估计的相合性及其渐近正态性,并给出模拟计算和应用实例以表明所提方法的有效性.     

变系数的周期性时间序列模型及其应用

存在于各个领域的时间序列不仅表现出周期性的特征还易受外界因素的影响,而且外界因素的影响并非一成不变,同时,部分时间序列的周期是未知的.对于这样的易受外界因素影响的周期性时间序列,本文旨在构造含有变系数函数的周期性序列模型.将经典的时间序列模型分解成一个含有未知参数的部分线性变系数模型,利用B样条逼近外生变量的变系数函数,借助带有l₀惩罚项的最小二乘回归得到未知周期、周期序列以及外生变量的影响系数的估计结果.本文还给出了估计量的理论性质,包括周期估计的相合性、周期序列估计和变系数函数估计的渐近性质.通过第4章的模拟,我们展现了本文方法的优越性.最后我们通过三个实际数据的应用展现了本文方法的实用性.     

Statistics of the Edge Green's Function for a One-Dimensional Disordered System with Binary or Uniform Diagonal Disorder

For a one-dimensional diagonally disordered chain, we study the statistics of the edge Green's function (EGF) constructed using the random matrix of the Hamiltonian of this system. We assume that the disorder is either binary or uniform. We show that the EGF distribution function is not analytic in the case of binary disorder and propose a simple algorithm for constructing this function. We calculate the EGF distribution function exactly on some interval in the case of uniform disorder and propose a simple, effective method for determining this function completely and for calculating the mean EGF. We verify all the obtained results using direct computer diagonalization and observe a good agreement.     

Optimal sampling and curve interpolation via wavelets

We propose a wavelet-based method for determining optimal sampling positions and inferring underlying functions based on the samples when it is known that the underlying function is Lipschitz. We first propose a Lipschitz regularity-based statistical model for data which are sampled from a Lipschitz curve. And then we propose a wavelet-based interpolation method for generating a Lipschitz curve given a set of points, and derive the optimal sampling positions.     

A nonmonotone derivative-free algorithm for nonlinear complementarity problems based on the new generalized penalized Fischer–Burmeister merit function

In this paper, we propose a new generalized penalized Fischer–Burmeister merit function, and show that the function possesses a system of favorite properties. Moreover, for the merit function, we establish the boundedness of level set under a weaker condition. We also propose a derivative-free algorithm for nonlinear complementarity problems with a nonmonotone line search. More specifically, we show that the proposed algorithm is globally convergent and has a locally linear convergence rate. Numerical comparisons are also made with the merit function used by Chen (J Comput Appl Math 232:455–471, 2009), which confirm the superior behaviour of the new merit function.     

A new refinement indicator for adaptive parameterization: Application to the estimation of the diffusion coefficient in an elliptic problem

We propose a new refinement indicator (NRI) for adaptive parameterization to determine the diffusion coefficient in an elliptic equation in two-dimensional space. The diffusion coefficient is assumed to be a piecewise constant space function. The unknowns are both the parameter values and the zonation. Refinement indicators are used to localize parameter discontinuities in order to construct iteratively the zonation (parameterization). The refinement indicator is obtained usually by using the first-order effect on the objective function of removing degrees of freedom for a current set of parameters. In this work, in order to reduce the computation costs, we propose a new refinement indicator based on the second-order effect on the objective function. This new refinement indicator depends on the objective function, and its first and second derivatives with respect to the parameter constraints. Numerical experiments show the high efficiency of the new refinement indicator compared to the standard one.     

A bundle-type algorithm for routing in telecommunication data networks

To optimize the quality of service through a telecommunication network, we propose an algorithm based on Lagrangian relaxation. The bundle-type dual algorithm is adapted to the present situation, where the dual function is the sum of a polyhedral function (coming from shortest path problems) and of a smooth function (coming from the congestion function).     

A primal—dual affine-scaling potential-reduction algorithm for linear programming

We propose a potential-reduction algorithm which always uses the primal—dual affine-scaling direction as a search direction. We choose a step size at each iteration of the algorithm such that the potential function does not increase, so that we can take a longer step size than the minimizing point of the potential function. We show that the algorithm is polynomial-time bounded. We also propose a low-complexity algorithm, in which the centering direction is used whenever an iterate is far from the path of centers.This paper is dedicated to Phil Wolfe on the occasion of his 65th birthday.     

A quasi-Newton bundle method based on approximate subgradients

In this paper we propose an implementable method for solving a nonsmooth convex optimization problem by combining Moreau-Yosida regularization, bundle and quasi-Newton ideas. The method we propose makes use of approximate subgradients of the objective function, which makes the method easier to implement. We also prove the convergence of the proposed method under some additional assumptions.     

一类新的求全局优化问题的填充函数

填充函数方法是一种寻找全局极小解的有效方法.本文首先对现有的填充函数进行研究分析,然后构造出一类新的填充函数,设计算法,并通过数值试验验证了该函数和算法的有效性.     

全局最优化问题的一个无参数的填充函数算法

本文研究了全局最优化问题.利用构造填充函数的方法,提出了一个新的无参数填充函数,它是目标函数的一个明确表达式.得到了一个新的无参数填充函数算法,数值试验结果表明该填充函数算法是有效的,从而推广了填充函数算法在求解全局最优化问题方面的应用.     

流面上的Navier-Stokes方程及其维数分裂方法

该文首先提出了流面和流层的概念,然后推导出了半测地坐标系下流层内的三维NS (Navier-Stokes)方程,以及流面上的二维NS方程.通过引入流面上的流函数,得到了流函数方程的非线性初边值问题,并讨论了方程解的存在性和唯一性.基于以上讨论,提出了求解三维NS方程的维数分裂方法, 并给出了算例.