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     

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.     

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。     

On a Ramanujan equation connected with the median of the gamma distribution

In this paper, we consider the sequence solving the Ramanujan equation

The three main achievements are the following. We introduce a continuous-time extension of and show its close connections with the medians of the distributions and the Charlier polynomials. We give upper and lower bounds for both and , in particular for , which are sharper than other known estimates. Finally, we show (and at the same time complete) two conjectures by Chen and Rubin referring to the sequence of medians .

     

The incoming statistical knowledge of undergraduate majors in a department of mathematics and statistics

Studies have shown that at the end of an introductory statistics course, students struggle with building block concepts, such as mean and standard deviation, and rely on procedural understandings of the concepts. This study aims to investigate the understandings entering freshman of a department of mathematics and statistics (including mathematics education), students who are presumably better prepared in terms of mathematics and statistics than the average university student, have of introductory statistics. This case study found that these students enter college with common statistical misunderstandings, lack of knowledge, and idiosyncratic collections of correct statistical knowledge. Moreover, they also have a wide range of beliefs about their knowledge with some of the students who believe that they have the strongest knowledge also having significant misconceptions. More attention to these statistical building blocks may be required in a university introduction statistics course.     

An evaluation of the multivariate dispersion charts with estimated parameters under non‐normality

Various charts such as |S|, W, and G are used for monitoring process dispersion. Most of these charts are based on the normality assumption, while exact distribution of the control statistic is unknown, and thus limiting distribution of control statistic is employed which is applicable for large sample sizes. In practice, the normality assumption of distribution might be violated, while it is not always possible to collect large sample size. Furthermore, to use control charts in practice, the in‐control state usually has to be estimated. Such estimation has a negative effect on the performance of control chart. Non‐parametric bootstrap control charts can be considered as an alternative when the distribution is unknown or a collection of large sample size is not possible or the process parameters are estimated from a Phase I data set. In this paper, non‐parametric bootstrap multivariate control charts |S|, W, and G are introduced, and their performances are compared against Shewhart‐type control charts. The proposed method is based on bootstrapping the data used for estimating the in‐control state. Simulation results show satisfactory performance for the bootstrap control charts. Ultimately, the proposed control charts are applied to a real case study.