关于mr(2,q)的一个新值

编码理论中关于寻找某一线性码的最大长度涉及到有限射影空间中关于t-blockingsets,(k,r-ares和caps集所含元素的个数的问题,本文研究了(k,r)-arc集的元素的个数,找到了使得(k,r)-arc集存在的最大k值,即mr(2,q)的一个新值,丰富了编码理论的相关内容。     

P(n，k)的计数及其良域

设P(n,k)为整数n分为k部的无序分拆的个数,每个分部≥1;P(n)为n的全分拆的个数.P(n,k)是用途广泛的、且又十分难予计算的数.本文证明了下述定理：当n＜k,P(n,k)=0;当k≤n≤2k,P(n,k)=P(n-k);当k=1,4≤n≤5,或者当k≥2,2k+1≤n≤3k+2,P(n,k)=P(n-k)-(?)P(t)还定义了P(n,k)的良城,因面可借助若干个P(n)的值,迅速地计算大量的P(n,k)的值.     

直线与双曲线交点问题的图解

<正>题目已知直线l:y=kx+1(k∈R),双曲线c:x~2-y~2=1.试求k的取值范围使直线l与双曲线c:(1)只有一个公共点,(2)有两个公共点,(3)没有公共点.分析直线与二次曲线的公共点个数问题即直线方程与曲线方程构成的方程组的解的个数问题,因此问题转化为确定方程组的解的个数问题.     

指数样本中多个异常值的Unmasking检验

指数样本中多个异常值的非一致性检验因受masking或swamping效应的影响而变得十分的困难和复杂，解决这一问题的关键在于K值的确定，传统的方法是无能为力的．本文基于变量选择的AIC准则的思想提出了异常值检验的一种新方法，它具有不预先指定k，计算简单且通过达到极大化MAIC就能达到确定k和消除检验中的masking或swamping的优点．还给出了易计算检验显著水平的统计量和公式．最后，通过实例的验证标明本文方法的有效性．     

一类带约束条件的集合之元素个数计数公式

本文给出了一类带不等式约束条件的集合 Bu(n,2n K)={(k1,k2…kn):{u k1≥2 u k1 k2≥2×2 … u k1 k2 … kn-1≥2(n-1) u k1 k2 … kn-1 kn=2n k n1,k1,k2…kn∈Ζ ,u,k∈Ζ}的元素个数的计算公式,并运用数学归纳方法给予了证明.     

一道国家集训题的导数证明

2005年国家集训题:从任意n(n≥2)个给定的正数a1,a2,…,an中,每项取k个数作乘积,所有这种乘积的算术平均值的k次方根,称为这n个数的k次对称平均,记为Bk.即Bk=a1a2…ak a1a3…ak 1 … an 1-k…an-1anCkn1k求证:若1≤k1相似文献   

数的n进制的一个定理及应用

1主要引理及定理引理1从0到n~2-1(2≤n≤10,n∈N)这n~2个数,在n进制中各位数字和被n除余数为k (0≤k≤n—1)的数的个数记为f_k(n),f_k(n)个余数相同的数的和记为S_k(n),则有: (1)f_k(n)=n,(2)S_k(n)=1/n·(n~2(n~2-1))/2.证明(1)将0到n~2-1这n~2个数依次排成n行,每行n个数,如下:     

三个或多个素变数的线性方程

推广了J.B.Friedlander和D.A.Goldston的结果,给出了素变数整系数线性方程a1p1 a2p2 … akpk=N(k≥3)解的个数的渐近公式.     

平衡单向分类随机效应模型中的多个异常值检验

该文研究平衡单向分类随机效应模型中多个异常值的检验问题. 在基于随机效应上的均值滑动模型下导出了似然比检验统计量, 并给出了其精确分布及水平异常值的检验过程. 在基于观测误差上的均值滑动模型下,利用得分检验统计量给出了多个异常值的检验过程.     

Boole函数的仿射分类与3-(λ,k,2~n)设计的构作(Ⅱ)

§1.引言 本文在[1]的基础上继续讨论二元域F_2上n维向量空间F_2~n中子集的仿射类的计数问题。 在文[1]中,我们对水平数l≤2,及子集大小k≤8的情形作了彻底的计算;在文[2]中对维数n=5的情形作了彻底的计算:解决了在这些限制条件下,仿射类类数及每个仿射类所含元素个数这两个问题。对更大的l,k,n值,要一般地完全解决这两个计数问题则是比较困难的,有待于更深入的讨论。     

应用RJMCMC方法识别线性模型异常点

传统线性模型异常点识别方法容易发生误判:正常点被归为异常点或者异常点被归为正常点.为解决此类问题,提出了应用逆跳马尔科夫蒙特卡洛方法识别异常点的思想,同时将其应用于实际数据加以检验,识别效果明显好于传统方法.     

线性模型参数的稳健化有偏估计

本文讨论复共线性和粗差同时存在时线性模型的参数估计问题,基于等价权原理提出了一个稳健有偏估计类（稳健压缩估计）,并且建立了稳健压缩估计的计算方法,为了满足实际问题的需要,构造了许多很有意义的稳健有偏估计,例如稳健岭估计、稳健主成分估计,稳健组合主成估计、稳健单参数主成分估计、稳健根方估计等等,最后通过一个算例表明,本文提出的稳健有偏估计具有既可克服复共线性影响又可抵抗粗差干扰的良好性质。     

Detecting multiple outliers in linear regression using a cluster method combined with graphical visualization

This paper provides a graphical visualization of multiple outliers based on a clustering algorithm using the minimal spanning tree, and proposes a modified version of this clustering algorithm for identifying multiple outliers. Graphical visualization is helpful for the classification of multiple outliers. It is shown that the proposed modified procedure preserves the performance of the clustering algorithm in identifying multiple outliers, but also reduces the problem of swamping of observations.     

指数分布场合下同时存在异常大和异常小值的检验

针对指数分布的场合 ,笔者从经典统计思想入手给出了”取中逐步推移检验法” ,较好地解决了同时存在异常大和异常小数据的检验问题     

Multiple outlier detection in multivariate data using self-organizing maps title

Summary  The problem of detection of multidimensional outliers is a fundamental and important problem in applied statistics. The unreliability of multivariate outlier detection techniques such as Mahalanobis distance and hat matrix leverage has led to development of techniques which have been known in the statistical community for well over a decade. The literature on this subject is vast and growing. In this paper, we propose to use the artificial intelligence technique ofself-organizing map (SOM) for detecting multiple outliers in multidimensional datasets. SOM, which produces a topology-preserving mapping of the multidimensional data cloud onto lower dimensional visualizable plane, provides an easy way of detection of multidimensional outliers in the data, at respective levels of leverage. The proposed SOM based method for outlier detection not only identifies the multidimensional outliers, it actually provides information about the entire outlier neighbourhood. Being an artificial intelligence technique, SOM based outlier detection technique is non-parametric and can be used to detect outliers from very large multidimensional datasets. The method is applied to detect outliers from varied types of simulated multivariate datasets, a benchmark dataset and also to real life cheque processing dataset. The results show that SOM can effectively be used as a useful technique for multidimensional outlier detection.     

基于Gibbs抽样的贝叶斯稳健ARMA模型研究

针对ARMA模型建模过程中模型识别和参数估计易受观测值异常点影响问题,构建了同时考虑加性异常点和更新性异常点的ARMA模型．运用基于Gibbs抽样的Markov Chain Monte Carlo贝叶斯方法,估计稳健ARMA模型参数,同步确定观测值中异常点的位置,辨别异常点类型．并利用我国人口自然增长数据进行仿真分析,研究结果表明：贝叶斯方法能够有效地识别ARMA序列的异常点．     

Allocating Vertex π-Guards in Simple Polygons via Pseudo-Triangulations

We use the concept of pointed pseudo-triangulations to establish new upper and lower bounds on a well known problem from the area of art galleries: What is the worst case optimal number of vertex π-guards that collectively monitor a simple polygon with n vertices? Our results are as follows: (1) Any simple polygon with n vertices can be monitored by at most \lfloor n/2 \rfloor general vertex π-guards. This bound is tight up to an additive constant of 1. (2) Any simple polygon with n vertices, k of which are convex, can be monitored by at most \lfloor (2n – k)/3 \rfloor edge-aligned vertexπ-guards. This is the first non-trivial upper bound for this problem and it is tight for the worst case families of polygons known so far.     

Choosing a Linear Model with a Random Number of Change-Points and Outliers

The problem of determining a normal linear model with possible perturbations, viz. change-points and outliers, is formulated as a problem of testing multiple hypotheses, and a Bayes invariant optimal multi-decision procedure is provided for detecting at most k (k > 1) such perturbations. The asymptotic form of the procedure is a penalized log-likelihood procedure which does not depend on the loss function nor on the prior distribution of the shifts under fairly mild assumptions. The term which penalizes too large a number of changes (or outliers) arises mainly from realistic assumptions about their occurrence. It is different from the term which appears in Akaikes or Schwarz criteria, although it is of the same order as the latter. Some concrete numerical examples are analyzed.     

A Review of Robust Regression and Diagnostic Procedures in Linear Regression

The concern over outliers is old since Bernoulli (see [12]), reviewed historically by [11] and updated with [10] in their encyclopedia textbook. James et al.~([46]) used simulation technique to compare some recent published outlier detection procedures.The history of adept and diagnosis of outliers is traced from old and presence comments. Theil-type or Rank, Brown-Mood, L_p, M, adaptive M, GM, and Trimmed-Winsorization estimators are the most popular estimators that we will review in this paper as an application to outlier accommodation. We will review and compare the most numerical and graphical displays based on residuals to flag outliers.