半相依回归系统的岭型主成分改进估计

对于一类半相依回归系统，本文提出了一种岭型主成分改进估计，并讨论了这种估计及相应的两步估计的优良性质，获得了若干深入的结果。     

半相依回归模型参数的协方差改进估计

本文研究了两个半相依回归系统的未知回归系数的估计问题。本文首先给出一种基于方差分量限定估计的两步协方差改进估计,并且给出了均方误差意义下优于最小二乘估计的条件。对于基于方差分量非限定估计的两步协方差改进估计,利用服从Wishart分布随机变量的可加性,本文给出了一种全新的估计形式,并且证明了该估计较文献中给出的两步协方差改进估计更加有效。     

相依样本情形下回归函数核估计的强相合性

设(x_i,y_i)。i-1,…,n,是从取值于R~d×R′的随机向量(x,y)中抽取的平稳,φ一混合样本,设E|y|<∞,记m(x)=E(y|X=x},我们在一定的条件下证明了m(x)的如下三种核估计的强相合性,同时对m_a~(1)(x)还讨论了收敛速度。     

相依误差下半参数回归模型的估计

本文在固定设计及相依误差下获得了半参数回归模型的参数估计的强相合性．     

截尾数据下一类半参数回归模型的估计

讨论了一类半参数回归模型y =x′β+g(t′α) +e .假定y被随机变量T右侧截尾 ,T与y独立 ,T～G。在G已知和未知两种情况下 ,构造了α、β和g(·) 的强相合估计     

相依样本一类非参数回归函数估计的强相合性

设Y_1,Y_2,…,Y_n是在固定点x_1,x_2,…,x_n的n个观察值,适合模型 Y_1=g(x_1)+ε_x,1≤i≤n (1) 这里g是R上的未知函数,{ε_1}为零均值的平稳、φ-混合过程,假定0=x_0≤x_1≤…≤x_(n-1)≤X_n=1。用 g_n(x)=sum from n-1 to ∞n Y_1H_n~(-1)(x_1-x_(x-x)K((x-x_1)/h_n) (2) 作为g(x)[x∈(0.1)]的估计。 本文讨论了g_n(x)的强相合性。     

关于两步估计的效率

本文首先指出[1]定理2证明中的一处错误。然后给出[1]中定义的三种两步估计效率的新下界,并将新的界与[1]中相应的下界进行了比较。     

PC准则下生长曲线模型回归参数阵岭估计的估计优良性

将ＰＣ准则推广应用于生长曲线模型参数阵的最小二乘估计和岭估计优劣性的比较,给出了岭估计在ＰＣ准则下优于最小二乘估计的条件。     

污染数据半参数回归模型的估计方法

考虑半参数回归模型ｙｊ＝ｘｊβ＋ｇ（ｔｊ）＋εｊ，ｊ＝１，２，…，ｎ其中（ｘｊ，ｔｊ）为取值于Ｒ×［０，１］上的固定设计，β为未知参数，ｇ是定义在［０，１］上的未知函数，εｊ为随机误差，Ｅεｊ＝０，Ｅε２ｊ＝σ２１．但ｙ１，…，ｙｎ受到另一独立同分布的随机变量序列ｕ１，…，ｕｎ两种不同方式的污染，ｕｊ与ｙｊ独立．本文利用矩估计方法给出两种污染方式下β、ｇ及污染参数的估计．     

NA相依样本的非参数核估计

假设非参数衰退模型Yi=g(Xi)+iε,其中残差{iε}是一个具有未知公共密度函数f(x)的NA相依样本,g(x)=E(Y+X=x)是未知衰退函数.今首先在残差基础上定义了非参数估计gn(x)和^fn(x),并在适当条件下证明了gn(x)和^fn(x)分别是g(x)和f(x)的强一致相合估计,同时给出了相应的收敛速度.     

一种光滑支持向量回归机新函数的研究

为支持向量回归机提供了一个新的光滑函数,即运用三次样条函数和复合函数的方法,得到一种新的光滑支持向量回归机——三次样条光滑支持向量回归机(TSSSVR).对该支持向量回归机的光滑函数进行了逼近性能和收敛性的分析,并说明该光滑函数比以往的光滑函数具有更高的逼近精度和收敛速度.     

Randomized residual-based error estimators for the proper generalized decomposition approximation of parametrized problems

This article introduces a novel error estimator for the proper generalized decomposition (PGD) approximation of parametrized equations. The estimator is intrinsically random: it builds on concentration inequalities of Gaussian maps and an adjoint problem with random right-hand side, which we approximate using the PGD. The effectivity of this randomized error estimator can be arbitrarily close to unity with high probability, allowing the estimation of the error with respect to any user-defined norm as well as the error in some quantity of interest. The performance of the error estimator is demonstrated and compared with some existing error estimators for the PGD for a parametrized time-harmonic elastodynamics problem and the parametrized equations of linear elasticity with a high-dimensional parameter space.     

An algorithm for computing a companion block diagonal form for a system of linear differential equations

In this paper we describe a new algorithm which reduces in a finite number of steps a linear system of differential equations to a companion block diagonal form. This form is particularly convenient if one wishes to compute invariants at singularities.     

一类五阶Korteweg-de-Vries方程的惟一连续性

惟一连续性是可积系统的重要性质之一,而初值问题解的性质与初值的光滑性密切相关.本文主要讨论了一类五阶KdV方程初值问题解的惟一连续性,证明了该初值问题的足够光滑的解,如果在一个非退化的时间区间内具有紧支集,那么该解恒为零.     

Numerical solution of a Cauchy problem for Laplace equation in 3-dimensional domains by integral equations

A numerical method based on integral equations is proposed and investigated for the Cauchy problem for the Laplace equation in 3-dimensional smooth bounded doubly connected domains. To numerically reconstruct a harmonic function from knowledge of the function and its normal derivative on the outer of two closed boundary surfaces, the harmonic function is represented as a single-layer potential. Matching this representation against the given data, a system of boundary integral equations is obtained to be solved for two unknown densities. This system is rewritten over the unit sphere under the assumption that each of the two boundary surfaces can be mapped smoothly and one-to-one to the unit sphere. For the discretization of this system, Weinert’s method (PhD, Göttingen, 1990) is employed, which generates a Galerkin type procedure for the numerical solution, and the densities in the system of integral equations are expressed in terms of spherical harmonics. Tikhonov regularization is incorporated, and numerical results are included showing the efficiency of the proposed procedure.     

Application of a new selection algorithm to the development of a wide-range equation of state for refrigerant R134a

Refrigerant R134a (1,1.1,2-tetrafuoroethane) is a leading substitute for refrigerant R12. As such, there has been worldwide activity to develop accurate wide-range equations of state for this fluid. In this study. we have developed a new selection algorithm for determining high-accuracy equations of state in the Helmholtz representation. This method combines least-squares regression analysis with simulated annealing optimization. Simulated annealing, unlike stepwise regression, allows for the controlled acceptance of random increases in the objective function. Thus, this procedure produces a computationally efficient selection algorithm which is not susceptible to the function-space local-minima problems present in a purely stepwise regression approach. Two equations are presented in this work and compared against experimental data and other high-accuracy equations of state for R134a. One equation was produced strictly by using stepwise a regression algorithm, while the other was produced using the simulated-annealing selection algorithm. In both cases the temperature dependence of the equations was restricted to have no terms whose exponents were greater than live.Paper presented at the Twelfth Symposium on Thermophysical Properties. June 19–24, 1994, Boulder, Colorado, U.S.A.     

A simple set of equations of state for process calculations and its application to R134a and R152a

This paper reports a useful set of equations which enables the consistent and reliable calculation of thermodynamic properties. This set of equations consists of a vapour pressure equation, an equation for the gas phase p, v, T properties, an equation giving the saturated liquid densities and an equation for the specific heat capacity in the ideal gas domain. These equations are of a simple structure because the critical region is excluded. Therefore, for a preliminary investigation only few experimental data points are required for parameter regression, which makes this set of equations suitable for ‘new’ refrigerants. The relationships for enthalpy and entropy are derived from these equations and evaluation procedures are summarized. Examples are given for the refrigerants R134a and R152a.