方向数据回归函数核估计平均偏差的指数界

本文讨论方向数据回归函数核估计的平均偏差,在关于应变量,核函数及窗宽的温和假定下得到了这类估计的平均偏差的指数界.     

可加模型低维分量估计平均偏差的指数界

设(X,Z,y),(X1,Z1,Y1),…,(Xn,Zn,Yn)为取值于Rp×Rq×R中的I.I.d.随机向量,E|Y|<∞,Y关于(X,Z)的回归函数m(x,z)△E(Y|(X,Z)＝(x,z))具有可加结构:m(x,z)＝m1(x)+m2(z).为估计可加分量,采用Linton&Nielsen(1995)提出的直接估计法,给出了可加分量的最近邻估计和核估计.在较弱的条件下,建立了可加分量最近邻估计和核估计的平均偏差的指数界.     

基于遍历函数型数据条件风险率函数的核估计

探究了在平稳遍历函数型数据下条件风险率函数的非参数核估计问题,本文基于N-W核估计的方法,构造响应变量Y在给定函数型解释变量X下的条件风险率函数非参数核估计,在一定条件下获得条件风险率函数非参数估计的偏差表达式.     

概率密度函数核估计的Bootstrap逼近

主要研究了密度函数核估计逼近的速度,用Bootstrap方法对核密度进行估计,在适当的条件下,进一步提高了密度核估计Bootstrap逼近的速度,所得到的结果使得密度核估计Bootstrap逼近的速度与密度函数及其导数之间的关系更加的明确.     

关于回归函数核估计的叠对数律

讨论了非参数回归函数的核估计，用核估计误差分解方法，较弱条件下，到了回归函数核估计的叠对数值。     

基于伴随次序统计量的回归函数核估计的矩相合性

回归函数的核估计的大样本性质,多年来一直受到众多学者的关注,且早期的回归函数的核估计均是基于原样本{(Xi, Yi), i≥1},本文基于二维随机样本{(Xi, Yi), i≥1}的伴随次序统计量Y[r,n],定义了回归函数的核估计,在一定条件下,获得了回归函数核估计的r阶矩相合性,推广了已有文献中的部分结果.     

基于核估计下概率密度函数的信度模型

结合核估计和信度理论的思想,建立了密度函数的Bayes模型,将条件密度函数的估计限定在核函数的线性组合中,通过最小化期望积分平方损失函数,得到了密度函数的信度估计,并研究了估计的统计性质,讨论了窗宽的最优选择方法;进而基于密度函数的信度估计,得到了各种保费原理中风险保费的信度估计,并与传统的信度估计进行了比较.     

强相关数据回归函数的小波估计

讨论了在强相关数据情形下对回归函数的小波估计，并且给出了估计量的均方误差的一个渐近展开表示式．对研究估计量的优劣，所推导的近似表示式显得非常重要．对一般的回归函数核估计，如果回归函数不是充分光滑，这个均方误差表示式并不成立．但对小波估计，即使回归函数间断连续，这个均方误差表示式仍然成立．因此，小波估计的收敛速度要比核估计来得快，从而小波估计在某种程度上改进了现有的核估计．     

球面数据核近邻估计的强相合性

该文绘出了球面数据密度函数的核近邻估计,通过对核估计与近邻估计相互关系的讨论,建立了核近邻估计的逐点强相合性及一致强相合性．     

某些Mercer核矩阵的权范数

借助整函数插值研究由函数的广义平移所生成的Mercer核矩阵及其逆矩阵权范数的上、下界估计问题,将定义在无限区间上整函数的广义平移所生成的Mercer核矩阵权范数界的估计转化为其Fourier-Bessel变换来估计.     

A new kernel function for SPH with applications to free surface flows

Smoothed particle hydrodynamics (SPH) is a popular meshfree Lagrangian particle method, which uses a kernel function for numerical approximations. The kernel function is closely related to the computational accuracy and stability of the SPH method. In this paper, a new kernel function is proposed, which consists of two cosine functions and is referred to as double cosine kernel function. The newly proposed double cosine kernel function is sufficiently smooth, and is associated with an adjustable support domain. It also has smaller second order momentum, and therefore it can have better accuracy in terms of kernel approximation. SPH method with this double cosine kernel function is applied to simulate a dam-break flow and water entry of a horizontal circular cylinder. The obtained SPH results agree very well with the experimental results. The double cosine kernel function is also comparatively studied with two frequently used SPH kernel functions, Gaussian and cubic spline kernel functions.     

基于不同核函数的非参数与参数利率模型的国债定价

以上海证券交易所的国债回购利率数据为样本,本文采用两种不同核函数:高斯核和抛物线核对非参数利率期限结构模型进行估计.结果显示:短期利率的密度函数是非正态的,扩散过程的漂移函数和扩散函数都是非线性的,高斯核比抛物线核对扩散函数拟合更平滑.然后,给出了基于非参数和参数利率模型的国债定价的方法,并对非参数利率模型、Vasicek模型、CIR模型、多项式样条静态模型进行国债定价预测比较与分析.     

计算再生核的Green函数方法

本文讨论了利用Green函数计算再生核的方法,在Wm2空间中利用再生核的和性质以及Green函数理论给出再生核构造的一般方法,并利用此方法计算出W32空间的再生核.     

From microscopic theory to macroscopic theory——symmetries and order parameters of rigid molecules

Density functional theory is used to describe the phase behaviors of rigid molecules. The construction of the kernel function is discussed. Excluded-volume potential is calculated for two types of molecules with C _2v symmetry. Molecular symmetries lead to the symmetries of the kernel function and the density function, enabling a reduction of configuration space. By approximating the kernel function with a polynomial, the system can be fully characterized by some moments corresponding to the form of the kernel function. The symmetries of the kernel function determine the form of the polynomial, while the coefficients are determined by the temperature and molecular parameters. The analysis of the impact of coefficients helps us to choose independent variables in the moments as order parameters. Combining the analysis and some simulation results, we propose a minimal set of order parameters for bent-core molecules.     

Convergence Properties of Generalized Fourier Series on a Parallel Hexagon Domain

A new Rogosinski-type kernel function is constructed using kernel function of partial sums Sn（f; t） of generalized Fourier series on a parallel hexagon domain Ω associating with threedirection partition. We prove that an operator Wn（f; t） with the new kernel function converges uniformly to any continuous function f（t） ∈ Cn（Ω） （the space of all continuous functions with period Ω） on Ω. Moreover, the convergence order of the operator is presented for the smooth approached function.     

Convex Kernel Underestimation of Functions with Multiple Local Minima

A function on Rⁿ with multiple local minima is approximated from below, via linear programming, by a linear combination of convex kernel functions using sample points from the given function. The resulting convex kernel underestimator is then minimized, using either a linear equation solver for a linear-quadratic kernel or by a Newton method for a Gaussian kernel, to obtain an approximation to a global minimum of the original function. Successive shrinking of the original search region to which this procedure is applied leads to fairly accurate estimates, within 0.0001% for a Gaussian kernel function, relative to global minima of synthetic nonconvex piecewise-quadratic functions for which the global minima are known exactly. Gaussian kernel underestimation improves by a factor of ten the relative error obtained using a piecewise-linear underestimator (O.L. Mangasarian, J.B. Rosen, and M.E. Thompson, Journal of Global Optimization, Volume 32, Number 1, Pages 1–9, 2005), while cutting computational time by an average factor of over 28.     

再生核移位勒让德基函数法求解分数阶微分方程

该文以再生核理论为基础,用移位Legendre多项式作为基函数构造了一个新的再生核空间,并给出了该空间下的再生核函数.与经典的再生核函数有所不同的是该空间下的再生核函数不再是分段函数,因此可以减小分数阶算子作用在核函数上时的计算量,使近似解更为精确.数值算例表明该方法的有效性.     

A note on the universal consistency of the kernel distribution function estimator

The problem of universal consistency of data driven bandwidth selectors for the kernel distribution estimator is analyzed. We provide a uniform in bandwidth result for the kernel estimate of a continuous distribution function. Our smoothness assumption is minimal in the sense that if the true distribution function has some discontinuity then the kernel estimate is no longer consistent.