固定设计下半参数回归模型核估计的渐近性质

研究一类新的半参数回归模型回归函数的核估计问题,其中误差项为一阶非参数自回归过程.通过重复利用Watson-Nadaraya核估计方法,构造了回归函数及误差回归函数的估计量分别为β,g(·)和ρ(·),在适当的条件下,证明了估计量β,g(·)和ρ(·)的渐近正态性.     

我国城乡居民消费与经济增长区域差异性的实证分析

遴选1996-2012年我国(除重庆、港、澳、台外)30个省(市)城镇和农村居民消费支出及国内生产总值的面板数据,基于非参数核估计方法,建立固定效应半参数面板数据模型,对我国东、中、西部城乡居民消费与经济增长关系的区域差异性进行实证分析.计算显示,运用半参数面板数据模型显著提高了估计的精度.分析结果表明,不论是城镇居民消费还是农村居民消费,对经济增长的促进作用均是东部高于中部、中部高于西部;且农村居民消费对经济增长的促进作用又大于城镇居民消费.     

复环面情形的Suita猜想

对任意复环面的情形证明了推广的Suita猜想,即απK≥c~2(α∈R),其中c是修正后的对数容度,K是对角线上的Bergman核.还阐明了对任意亏格≥2的紧Riemann面情形的公开问题.文中结果的证明部分地依赖于椭圆函数理论.     

一个新的求解半正定规划问题的原始对偶内点算法

选择合适的核函数对设计求解线性规划与半正定规划的原始对偶内点算法以及复杂性分析都十分重要.Bai等针对线性规划提出三种核函数,并给出求解线性规划的大步迭代复杂界,但未给出数值算例验证算法的实际效果(Bai Y Q,Xie W,Zhang J.New parameterized kernel functions for linear optimization.J Global Optim,2012.DOI 10.1007/s10898-012-9934-z).基于这三种核函数设计了新的求解半正定规划问题的原始对内点算法.进一步分析了算法关于大步方法的计算复杂性界,同时通过数值算例验证了算法的有效性和核函数所带参数对计算复杂性的影响.     

Perturbation of the eigenvectors of the graph Laplacian: Application to image denoising

Patch-based denoising algorithms currently provide the optimal techniques to restore an image. These algorithms denoise patches locally in “patch-space”. In contrast, we propose in this paper a simple method that uses the eigenvectors of the Laplacian of the patch-graph to denoise the image. Experiments demonstrate that our denoising algorithm outperforms the denoising gold-standards. We provide an analysis of the algorithm based on recent results on the perturbation of kernel matrices (El Karoui, 2010) [1], [2], and theoretical analyses of patch denoising algorithms (Levin et al., 2012) [3], (Taylor and Meyer, 2012) [4].     

A collocation method based on reproducing kernel for a modified anomalous subdiffusion equation

In this article, we proposed a collocation method based on reproducing kernels to solve a modified anomalous subdiffusion equation problem. We give constructively the ‐approximate of the equation whose coefficients are determined optimally by solving a system of linear equations. The final numerical experiments demonstrate that the proposed method is simple, effective, and easy to implement. Copyright © 2012 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 30: 289–300, 2014     

刻度指数族参数的经验Bayes估计及收敛速度

本文在刻度平方误差损失函数下导出了刻度指数族分布中参数的Bayes估计.利用核估计的方法构造了参数的经验Bayes估计,在适当条件下得到了经验Bayes估计的收敛速度,推广了文献中的相关结果.     

刻度指数族参数的经验Bayes估计及收敛速度

本文在刻度平方误差损失函数下导出了刻度指数族分布中参数的Bayes 估计. 利用核估计的方法构造了参数的经验Bayes 估计, 在适当条件下得到了经验Bayes 估计的收敛速度, 推广了文献中的相关结果.     

Automorphisms of normal quasi-circular domains

It was shown by Kaup that every origin-preserving automorphism of quasi-circular domains is a polynomial mapping. In this paper, we study how the weight of quasi-circular domains and the degree of such automorphisms are related. By using the Bergman mapping, we prove that every origin-preserving automorphism of normal quasi-circular domains in C²${\mathbb{C}}^2$ is linear.