A Note on the Comedian for Elliptical Distributions

The comedianCOM(X, Y) of random variablesX,Yis a median based robust alternative to the covariance ofXofY. For the bivariate normal case it is known thatCOM(X, Y), standardized by the median absolute deviations ofXandY, is a symmetric, strictly increasing and continuous function of the correlation coefficientρwith range [−1, 1] and can therefore serve as a robust alternative toρ. We show that this result, which is not true in general, extends to elliptical distributions even in the case where moments ofX,Ydo not exist.     

LOCAL MEDIAN ESTIMATION OF VARIANCE FUNCTION

This paper considers local median estimation in fixed design regression problems. The proposed method is employed to estimate the median function and the variance function of a heteroscedastic regression model. Strong convergence rates of the proposed estimators are obtained. Simulation results are given to show the performance of the proposed methods.     

红外图像空间噪声分析和预处理方法改进

讨论了基于天空背景下红外图像空间噪声组成，分析了各种空间噪声的形成原因,给出了红外图像噪声类型及其对图像质量的不同影响。分析结果认为红外图像空间噪声主要为高斯噪声和椒盐噪声。综合考虑均值法和中值法在处理噪声类型上的不同，提出了一种基于简单阈值的改进型中值法。对于不同的阈值，其算子有所不同。而M×N处理区域内每一点算子的权值取决于区域灰度中值，该点灰度越接近中值权值越大。处理后的图像背景更平滑，信噪比和改进的峰值信噪比提高了1.2dB以上，表明改进型中值法优于传统滤波方法。     

基于FPGA的实时中值滤波器设计

在图像生成和采集过程中引入的各种噪声会使图像质量变差。为了实现对图像的实时预处理，首先介绍中值滤波器的基本原理和算法，然后在现场可编程门阵列（FPGA）上根据中值滤波的根基数算法，采用流水技术设计一种快速实时中值滤波器，给出按行输出的图像处理过程中存储前2行图像数据的方法。仿真结果表明：该中值滤波器可实时完成CCD输出图像的预处理，达到了抑制噪声及保持图像细节的目的。     

不等式的证明

不等式的证明方法很多 ,本文给出了几种常用方法 ,通过这些方法 ,可以比较简洁 ,快速的解决一些不等式证明问题     

Second order asymptotic comparison of estimators of a common parameter in the double exponential case

Summary The problem to estimate a common parameter for the pooled sample from the double exponential distributions is discussed in the presence of nuisance parameters. The maximum likelihood estimator, a weighted median, a weighted mean and others are asymptotically compared up to the second order, i.e. the ordern ^−1/2 with the asymptotic expansions of their distributions. University of Electro-communications     

Addendum to “a third-order optimum property of the maximum likelihood estimator”

A third-order optimum property of the maximum likelihood estimator is extended to not necessarily symmetric loss functions under an appropriate restriction on the class of competing estimators.     

Smoothness of Nonlinear Median-Interpolation Subdivision

We give a refined analysis of the Hölder regularity for the limit functions arising from a nonlinear pyramid algorithm for robust removal of non-Gaussian noise proposed by Donoho and Yu [6,7,17]. The synthesis part of this algorithm can be interpreted as a nonlinear triadic subdivision scheme where new points are inserted based on local quadratic polynomial median interpolation and imputation. We introduce the analogon of the Donoho–Yu scheme for dyadic refinement, and show that its limit functions are in C for >log₄(128/31)=1.0229.... In the triadic case, we improve the lower bound of >log₂(135/121)=0.0997... previously obtained in [6] to >log₃(135/53)=0.8510.... These lower bounds are relatively close to the anticipated upper bounds of log₂(16/7)=1.1982... in the dyadic, respectivly 1 in the triadic cases, and have been obtained by deriving recursive inequalities for the norm of second rather than first order differences of the sequences arising in the subdivision process.     

无重复因析试验中散度效应的ML估计

在无重复因析试验中,若因子A,B的散度效应显著,则不论其交互效应AB的散度效应是否显著,其散度效应的现有估计常常是有偏的,从而导致其被错误地识别为显著效应.提出了散度效应的一种新的估计方法(称为ML估计),并给出了ML估计的方差的精确表达形式,证明了在一类模型中,交互效应AB的散度效应的ML估计是无偏的.最后,将ML估计与现有的常用估计进行了比较.     

一种改进的基于分水岭的图像分割算法

针对分水岭算法过分割现象,提出一种综合分水岭算法、中值过滤算法和归一化割算法的改进算法。该算法首先应用改进型的中值过滤算法对图像进行适当的除噪;然后通过分水岭变换对图像进行了初步分割,最后使用归一化割算法进行图像精度分割。算法集合了分水岭算法、中值过滤算法及归一化割算法的优点,既较好地解决了分水岭算法中过度分割的问题,又降低了归一化割算法的时间复杂度。实验结果表明该算法是一种切实可行的图像分割方法。