基于残差加权经验过程方法的自回归模型分布变点监测

Change monitoring of distribution in time series models is an important issue.This paper proposes a procedure for monitoring changes in the error distribution of autoregressive time series,which is based on a weighed empirical process of residuals with weights equal to the regressors.The asymptotic properties of our monitoring statistic are derived under the null hypothesis of no change in distribution.The finite sample properties are investigated by a simulation.As it turns out,the procedure is not only able to detect distributional changes but also changes in the regression coefficient and mean.Finally,we apply the statistic to a groups of financial data.     

无穷方差厚尾过程变点的小波估计

研究随机设计下噪声为厚尾随机变量时非参数函数中的变点估计问题.首先,通过设计变换将随机设计转化为等间距固定设计,进而利用小波方法估计变换后的变点的位置,再利用逆设计变换求得随机设计下变点位置的估计,并给出估计的收敛速度.模拟研究结果说明对于无穷方差厚尾过程中的变点估计问题小波方法是有效的.     

厚尾相依序列的均值变点估计

本文研究了厚尾相依序列的均值变点估计. 证明了变点的CUSUM估计的一致性并得到了收敛速度.在方差无穷的情况下推广了H\'{a}jek--R\'{e}nyi不等式.     

两类索赔相关风险模型的罚金折现期望函数

考虑两类索赔相关风险模型.两类索赔计数过程分别为独立的广义Poisson过程和广义Erlang(2)过程.得到了该风险模型的罚金折现期望函数满足的积分微分方程及该函数的Laplace变换的表达式,且当索赔额均服从指数分布时,给出了罚金折现期望函数及破产概率的明确表达式.     

一类线性回归模型中核估计的渐近性质

考虑固定设计下具有一阶非参数自回归误差的线性模型,构造了参数和非参数函数的N-W核估计,在适当的条件下,证明了参数估计的强相合性,同时给出了非参数函数估计的渐近正态性.     

ARCH模型的多变点检验

研究自回归条件异方差(ARCH)模型的多变点检验问题.提出一种拟似然比检验统计量,并在原假设下给出统计量的极限分布.在假设检验过程中得到变点个数的一致估计.数值模拟与实例分析说明了方法的合理性.     

无穷方差厚尾过程中非参数函数的小波估计

研究无穷方差厚尾过程中含有变点的非参数函数的估计问题。通过小波方法给出变点位置的估计值并得到其收敛速度。在已知变点估计值的基础上,将截尾方法与小波压缩方法相结合得到非参数函数的估计值。模拟研究结果说明对于无穷方差厚尾过程中的函数估计问题小波方法是有效的。     

非线性模型滞后相依的广义互信息检验

The general mutual information （GMI） and general conditional mutual information （GCMI） are considered to measure lag dependences in nonlinear time series. Both of the measures have the property of invariance with transform. The statistics based on GMI and GCMI are estimated using the correlation integral. Under the hypothesis of independent series, the estimators have Gaussian asymptotic distributions. Simulations applied to generated nonlinear series demonstrate that the methods appear to find frequently the correct lags.     

Image registration based on matrix perturbation analysis using spectral graph

We present a novel perspective on characterizing the spectral correspondence between nodes of the weighted graph with application to image registration. It is based on matrix perturbation analysis on the spectral graph. The contribution may be divided into three parts. Firstly, the perturbation matrix is obtained by perturbing the matrix of graph model. Secondly, an orthogonal matrix is obtained based on an optimal parameter, which can better capture correspondence features. Thirdly, the optimal matching matrix is proposed by adjusting signs of orthogonal matrix for image registration. Experiments on both synthetic images and real-world images demonstrate the effectiveness and accuracy of the proposed method.     

Segmentation of synthetic aperture radar image using multiscale information measure-based spectral clustering

A multiscale information measure （MIM）, calculable from per-pixel wavelet coefficients, but relying on global statistics of synthetic aperture radar （SAR） image, is proposed. It fully exploits the variations in speckle pattern when the image resolution varies from course to fine, thus it can capture the intrinsic texture of the scene backscatter and the texture due to speckle simultaneously. Graph spectral segmen- tation methods based on MIM and the usual similarity measure are carried out on two real SAR images. Experimental results show that MIM can characterize texture information of SAR image more effectively than the commonly used similarity measure.