M-Cross-Validation in Local Median Estimation

M-cross-validation criterion is proposed for selecting a smoothing parameter in a nonparametric median regression model in which a uniform weak convergency rate for the M-cross-validated local median estimate, and the upper and lower bounds of the smoothing parameter selected by the proposed criterion are established. The main contribution of this study shows a drastic difference from those encountered in the classical L2-, L1- cross-validation technique, which leads only to the consistency in the sense of the average. Obviously, our results are novel and nontrivial from the point of view of mathematics and statistics, which provides insight and possibility for practitioners substituting maximum deviation for average deviation to evaluate the performance of the data-driven technique.     

L2—cross—validation最近邻中位数估计的渐近最优性

本文研究固定设计点模型的最近邻中位数估计的光滑参数的选择问题。在一定的正则性条件下得到了Ｌ２－ｃｒｏｓｓ－ｖａｌｉｄａｔｉｏｎ最近邻中位数估计的渐近最优性。同时还得到了最近邻中位数估计的弱Ｂａｈａｄｕｒ表示。     

Median Unbiased Estimation of Bivariate Predictive Regression Models with Heavy-tailed or Heteroscedastic Errors

In this paper, we consider median unbiased estimation of bivariate predictive regression models with non-normal, heavy-tailed or heteroscedastic errors. We construct confidence intervals and median unbiased estimator for the parameter of interest. We show that the proposed estimator has better predictive potential than the usual least squares estimator via simulation. An empirical application to finance is given. And a possible extension of the estimation procedure to cointegration models is also described.     

具有重尾或异方差误差的双变量预测回归模型的中位无偏估计

In this paper, we consider median unbiased estimation of bivariate predictive regression models with non-normal, heavy-tailed or heterescedastic errors. We construct confidence intervals and median unbiased estimator for the parameter of interest. We show that the proposed estimator has better predictive potential than the usual least squares estimator via simulation. An empirical application to finance is given. And a possible extension of the estimation procedure to cointegration models is also described.     

Bayesian Variable Selection for Median Regression

When the data has heavy tail feature or contains outliers, conventional variable selection methods based on penalized least squares or likelihood functions perform poorly. Based on Bayesian inference method, we study the Bayesian variable selection problem for median linear models. The Bayesian estimation method is proposed by using Bayesian model selection theory and Bayesian estimation method through selecting the Spike and Slab prior for regression coefficients, and the effective posterior Gibbs sampling procedure is also given. Extensive numerical simulations and Boston house price data analysis are used to illustrate the effectiveness of the proposed method.     

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??When the data has heavy tail feature or contains outliers, conventional variable selection methods based on penalized least squares or likelihood functions perform poorly. Based on Bayesian inference method, we study the Bayesian variable selection problem for median linear models. The Bayesian estimation method is proposed by using Bayesian model selection theory and Bayesian estimation method through selecting the Spike and Slab prior for regression coefficients, and the effective posterior Gibbs sampling procedure is also given. Extensive numerical simulations and Boston house price data analysis are used to illustrate the effectiveness of the proposed method.     

盒子型区域上变分不等式的一个光滑牛顿法(英文)

The box constrained variational inequality problem can be reformulated as a nonsmooth equation by using median operator.In this paper,we present a smoothing Newton method for solving the box constrained variational inequality problem based on a new smoothing approximation function.The proposed algorithm is proved to be well defined and convergent globally under weaker conditions.     

Some extension of Haldane's multivariate median and its application

Summary Some extension of Haldane's multivariate median is carried out by minimization principle of a specified distance function. Then, making use of the median, three types of measures of multivariate skewness are introduced and their asymptotic null distributions are obtained.     

On topological types of ordered median functions

An ordered median functions is a continuous piecewise-linear function. It is well known that in finite dimensional spaces every continuous piecewise-linear function admits a max-min representation in terms of its linear functions. An explicit representation of an ordered median function in max-min form is given by the authors and will appear in a forthcoming issue of this journal. Based on this representation, we give a topological classification of ordered median functions through their simplicial complex of ascent (resp. descent) cones.     

网络选址中对中心点和中位点问题的综合考虑

针对目前网络选址研究中大多分别研究中心点和中位点的片面性,分析综合考虑中心点和中位点的网络选址问题.首先提出对中心点和中位点进行综合考虑的问题,然后通过两个具体的实例,分别建立了综合考虑网络选址的中心点和中位点、绝对中心点和绝对中位点的两个模型,并给出了相应的求解方法、步骤和结果.     

两阶段抽样中位值-极差联合控制图

在统计质量控制中,通常利用中位值图和极差图来控制生产过程的均值和方差.建立了两阶段中位值和极差联合控制图,在第一阶段抽取一个样本进行检测,如果过程处于控制,就停止抽样,否则进行第二阶段抽样检测.文中将其与其他类型的中位值-极差联合控制图做了比较.结果表明,两阶段抽样控制图能更有效地检测生产过程的波动变化.     

提升格式下几种去噪方法的比较

本文比较了四种去噪声的效果,利用提升格式设计的灵活性,通过预算子或更新算子的设计最优匹配特定的信号,比较了软阈值函数、硬阈值函数、比例萎缩LAWML法和小波域中值滤波四种去噪方法.     

估计感度分布中位数的两阶段优化序贯试验设计方法研究

感度试验在爆炸科学领域有非常广泛的应用,其中位数是含能材料的一个关键性能指标.高效估计感度分布中位数是实际工程应用中的重要问题.文章提出一种两阶段的优化序贯试验设计方法来估计感度分布的中位数,并将正交设计与两阶段优化序贯试验设计方法相结合给出了筛选影响含能材料安定性重要因子的试验设计方法.广泛的模拟比较验证了所提方法在小样本情况下可以获得感度分布中位数的准确估计,并且对模型假设和初始参数猜测具有一定的稳健性.当因子效应不是太小的时候,因子筛选方法可以准确地筛选出有显著影响的因子.     

广义Taylor中值函数若干分析性质

文[2-8]对微分中值定理及Taylor定理"中间点"的渐近性质进行了研究,本文在此基础上,给出了"广义Taylor中值函数"的定义,对"广义Taylor中值函数"的分析性质进行了系统的讨论,证明了"广义Taylor中值函数"的单调性、可积性、连续性、可微性等分析性质.     

Online signal extraction by robust linear regression

Summary  In intensive care, time series of vital parameters have to be analysed online, i.e. without any time delay, since there may be serious consequences for the patient otherwise. Such time series show trends, slope changes and sudden level shifts, and they are overlaid by strong noise and many measurement artefacts. The development of update algorithms and the resulting increase in computational speed allows to apply robust regression techniques to moving time windows for online signal extraction. By simulations and applications we compare the performance of least median of squares, least trimmed squares, repeated median and deepest regression for online signal extraction.     

Extension of Mood’s median test for survival data

Mood’s median test for testing the equality of medians is a nonparametric approach, which has been widely used for uncensored data in practice. For survival data, many nonparametric methods have been proposed to test for the equality of survival curves. However, if the survival medians, rather than the curves, are compared, those methods are not applicable. Some approaches have been developed to fill this gap. Unfortunately, in general those tests have inflated type I error rates, which make them inapplicable to survival data with small sample sizes. In this paper, Mood’s median test for uncensored data is extended for survival data. The results from a comprehensive simulation study show that the proposed test outperforms existing methods in terms of controlling type I error rate and detecting power.     

Asymptotics for the Tukey Median

The asymptotic distribution of the Tukey median has recently been obtained by Nolan in a bivariate setting and by Bai and He in the general multivariate case. To establish their theorem, these authors made a strong symmetry hypothesis on the distribution and, in the case of Bai and He, assumed the existence of a density function with a gradient satisfying a finite-moment condition. This paper extends the above result by deriving the asymptotic distribution of the above location estimate without making any symmetry or differentiability assumption on the distribution.     

基于小波域中值滤波和运动估计的去隔行算法

本文提出了一种新的自适应去隔行算法,该方法首先将小波分解引入到去隔行算法的预处理阶段,然后利用运动估计以及混合中值滤波的特点,充分考虑相邻像素间的方向空间相关性,有效保持图像中的边界部分,并减小了运动补偿插值后的误差,尤其是对纹理信息丰富的地方得到了很好的插值效果.实验结果表明,无论是从客观上的信噪比还是主观测评来分析,图像的效果比传统的算法有了提高,能更好的满足人类对画面质量的要求.     

双侧截断数据的中位数回归(英文)

在很多实际应用中,个体寿命时间可能被同时左截断与右截断.本文在左右截断变量都能被观察到的假设下,提出了一种半参数推断方法,来分析协变量对于相应寿命时间或其某种变换的中位数的影响,并讨论了所得估计量的渐近性质.此外,本文还提供了一种基于经验似然的回归参数推断方法,并讨论了将这些方法推广到经典双侧截断数据的可能性.一些模拟计算被用于展示这些方法的有效性.