刀切Von-Mises统计量

设 X_1、X_2,…,X_n…为一系列独立同分布的随机变量,它们服从分布 F_θ。设(?)(x_1,x_2,…x_m)是关于 m 个变元 x_1,…x_m 对称的函数。定义以(?)为核的 U-统计量为U_n:(?)~(-1)∑_1≤α_1<…<α_m≤n(?)(X_α_1,…,X_α_m) (n≥m) (1)相应的 Von-Mises 统计量为     

PP聚类的众数指标及最优方向估计的相合性

在[5]中我们提出了一种PP聚类指标——众数指标,并在一定条件下得到了最优方向估计的渐近分布.本文关心的是PP众数指标及其最优方向估计的相合性以及收敛速度.首先,我们回顾一下[5]中提出的两种众数指标.设有P元随机向量X,具正定的协方差阵∑_0,期望μ_0,且α方向上的边缘密度为 g(a;t),t∈R~1.设X_1,…,X_n为X的n     

几类PP型检验统计量的性质

投影寻踪(Projection Pursuit,简称 PP)方法是一种新兴的处理高维数据的统计方法.其主要思想是:把高维数据(p 维),X_1,X_2,…,X_n 投影到低维空间(通常是一维),设 Q 为一能反映我们感兴趣的统计性质的指标(一般为分布的泛函).对于每个 P 维方向,计算出 Q(a~TX_1,a~TX_2,…,a~TX_n)找出使 Q(a~TX_1,a~TX_2,…,a~TX_n)达到最大的方向 a_0,通过研究数据 a_0~TX_1,…,a_0~TX_n 的性质,来了解原数据 X_1,X_2,…,X_n 的性质.详细论述见成平、李国英等[2],Huber[4].     

重调和函数的平均值性质

设Ω是 C~n 中的有界对称域,f=u jv 是Ω上的全纯函数,f(0)∈R.记(?)_(p,q,α)=(?)(1-r)~(qα-1)M_p~(?)(r,f)dr(?)~(1/q).本文证明了(?)_(p,q,α),≤C(?)_(p,q,a)(00).     

加权平方和损失下线性估计的可容许性

1980年,Berger讨论了Γ分布尺度参数的通常估计的容许性向题.本文在此基础上讨论Γ分布尺度参数的线性估计的容许性问题,即 例1 设X_1和X_2相互独立,X_1～Γ(α_1,β_1~(-1)),X_2～Γ(α_2,β_2~(-1))α_1和α_2是已知的正常数,β=(β_1,β_2)′∈R~ ×R~ 是未知的参数.取β的估计为线性估计     

点到集映象族二步算法的弱收敛性

1.引言文献[1]首次提出了仅与空间的拓扑性质有关的点到集映象族一步算法的弱收敛条件,这些条件是对[2]～[7]中相应结果的改进和推广。本文将这些条件推广到点到集映象族的二步算法中去,得到了相应的结果,下面仅给出几个假设条件与部分定理等。 2.二步算法设X_0、X_1(?)R~n为紧集,M为X_0的子集,{⊿_ρ|ρ≥0}、{F_t|t≥0}分别为从X_0到2~(X_1)和从X_0×X_1到2~(X_(?)的点到集映象族,     

最近邻判别法中错误概率估计的强收敛速度(英文)

本文考虑最近邻判别法中错误概率估计的强收敛速度.设(X,θ),(X_1,θ_1),…,(X_n,θ_n)为取值于 R~m×{1,2,…,M}的 i.i.d.样本,m≥1,M≥2为正整数.记θ′_n 为θ的最近邻判别,错判概率 R_n=p(θ′_n≠θ),恒有(?)R_n=R.(?)_n 为基于 X,并借助于训练样本(X_1,θ_1),…,(X_nθ_n)的 R_n 的估计量.我们证明了在一组条件下,及对适当选取的α>0,有(?)_n-R=0(1/(n~α)).     

关于多维平稳序列的一个结果

是一个 m 维宽平稳随机向量序列,且 Ex_i=0(零向量),i=1,2,….易知(?)与 i 无关,且(?)(τ)~T 是一个 m 阶矩阵(A~T 表示 A 的转置矩阵).又(?)特别(?)(0)=(?)(0)~T 是每个随机向量的协方差阵.今有 n+1个 m 维宽平稳的随机向量 X_1,…,X_(n+1).令     

可换序列变叙项极值的渐近分布

设X_(1,n) …,X_(N,n)是可换r. V. 无穷序列的一段,X_(1,n)~＊≤…≤X_(N,n)~＊为其顺序统计量,N=N(n)是与这些X(1,N)独立的正整值r. V.,n=1,2,….当k_n·n~(-(?))→α(0<α<∞,0<(?)<∞)时,本文得出了X_(N-k_n 1m)~＊的渐近分布。     

均匀分布族U(θ_1,θ_1+θ_2)参数的最佳仿射同变估计之非容许性

设随机变量其密度函数为,其中θ_2>0,-∞<θ_1<+∞均为未知参数。X_1,X_2,…,X_n是抽自X的简单子样;X_(1),X_(2),…,X_(n)为由此产生的顺序统计量。我们在损失函数与 之下分别考虑θ_1与θ_2的估计问题。其相应的风险函数分别记为与。众所周知,θ_1与θ_2的最佳仿射同变估计分别为与其中     

The asymptotic power of rank tests under scale-al ternatives including contaminated distributions

Summary The alternative hypothesis of translated scale for the classical non-parametric hypothesis of equality of two distribution functions in the two-sample problem is extended to a scale-alternative including contamination. The asymptotic power of rank tests and the two-sampleF-test under contiguous sequences of the alternatives is derived and asymptotic relative efficiency of these rank tests with respect to theF-test is investigated. It is found that some of the rank tests have reasonably high asymptotic powers satisfied enough.     

PP multivariate random weighting method

According to the Projection Pursuit (PP) method and the random weighting method, we propose a PP random weighting method, and set up the asymptotic distribution theory and strong limit theorem of PP random weighting empirical process. Applying this method, we obtain two kinds of goodness-of-fit test for a multivariate distribution function, i.e., we get the random weighting approximations of PP Kolmogorov Smirnov statistics (PPKS) and PP Smirnov Cramér Von Mises statistics (PPSC), we prove that the asymptotic distribution of PPKS and PPSC are the same as those of their respective random weighting approximations.Supported by the National Natural Science Foundation of China.     

An asymptotic expansion for product integration applied to Cauchy principal value integrals

Product integration methods for Cauchy principal value integrals based on piecewise Lagrangian interpolation are studied. It is shown that for this class of quadrature methods the truncation error has an asymptotic expansion in integer powers of the step-size, and that a method with an asymptotic expansion in even powers of the step-size does not exist. The relative merits of a quadrature method which employs values of both the integrand and its first derivative and for which the truncation error has an asymptotic expansion in even powers of the step-size are discussed.     

Asymptotic distributions in the projection pursuit based canonical correlation analysis

In this paper, associations between two sets of random variables based on the projection pursuit (PP) method are studied. The asymptotic normal distributions of estimators of the PP based canonical correlations and weighting vectors are derived.     

Heteroscedasticity and/or Autocorrelation Checks in Longitudinal Nonlinear Models with Elliptical and AR（1） Errors

The aim of this paper is to study the tests for variance heterogeneity and/or autocorrelation in nonlinear regression models with elliptical and AR(1) errors. The elliptical class includes several symmetric multivariate distributions such as normal, Student-t, power exponential, among others. Several diagnostic tests using score statistics and their adjustment are constructed. The asymptotic properties, including asymptotic chi-square and approximate powers under local alternatives of the score statistics, are studied. The properties of test statistics are investigated through Monte Carlo simulations. A data set previously analyzed under normal errors is reanalyzed under elliptical models to illustrate our test methods.     

基于投影偏度和投影峰度的投影寻踪自助法的正态性检验

本文研究了多元分布的正态性检验问题,用投影寻踪自助法,获得了投影偏度和投影峰度正态性检验统计量,证明了在零假设成立时,所提出的偏度和峰度检验统计量的极限分布为一高斯过程的上界.为计算机模拟计算提供了有力的手段和依据.     

On the jaccard similarity test

A new class of tests for testing the homogeneity of two independent polynomial samples is proposed. Our tests are a natural extension of those based on Jaccard's index of similarity. The theory of separable statistics is applied. We investigate asymptotic powers of these tests. The results of numerical analysis allow us to select the asymptotically optimal test of similarity within this class. Translated fromStatisticheskie Metody Otsenivaniya i Proverki Gipotez, pp. 42–51, Perm, Russia, 1995.     

Steplike contrast structure in a singularly perturbed system of equations with different powers of small parameter

A singularly perturbed boundary value problem for a system of equations with different powers of a small parameter is considered in the one-dimensional case. The asymptotic behavior and existence of a solution with an internal transition layer are analyzed. The asymptotics are substantiated using the asymptotic method of differential inequalities.     

协方差矩阵的齐性检验

基于ＰＰ技术、Ｂｏｏｔｓｔｒａｐ方法和数论方法,对于ｋ个总体协方差矩阵相等的检验,给出了ＰＰ型检验统计量,并讨论了它的渐近分布和Ｂｏｏｔｓｔｒａｐ逼近,最后给出了一些实际模拟结果。     

A class of PP l-statistics for tests

Applying projection pursuit (PP) techniques, this paper takes L-statistics as projection indices to construct a class of statistics for multivariate tests. The asymptotic distributions of the test statistics under null hypothesis are derived theoretically. Some simple applications to location and dispersion problems are given.This project is supported by the National Natural Science Foundation of China.