Permutation Tests for Reflected Symmetry

The paper presents a permutation procedure for testing reflected (or diagonal) symmetry of the distribution of a multivariate variable. The test statistics are based in empirical characteristic functions. The resulting permutation tests are strictly distribution free under the null hypothesis that the underlying variables are symmetrically distributed about a center. Furthermore, the permutation tests are strictly valid if the symmetric center is known and are asymptotic valid if the center is an unknown point. The equivalence, in the large sample sense, between the tests and their permutation counterparts are established. The power behavior of the tests and their permutation counterparts under local alternative are investigated. Some simulations with small sample sizes (?20) are conducted to demonstrate how the permutation tests works.     

Invariant Tests for Covariance Structures in Multivariate Linear Model

The null hypothesis that the error vectors in a multivariate linear model are independent is tested against the alternative hypothesis that they are dependent in some specified manner. This dependence is assumed to be due to common random components or autocorrelation over time. The testing problem is solved by classical invariance arguments under multinormality. The most powerful invariant test usually depends on the particular alternative and may even lack a closed form expression. Then the locally best test is derived. The power is maximized at the null hypothesis in the direction of some alternative. In most applications the direction where the maximization is performed does not enter the test. Then the locally uniformly best test exists. Several applications are outlined.     

全错位排列问题的基于芯片的DNA计算模型

全错位排列问题作为组合数学中一个重要的问题,到目前为止还没有好的算法.应用DNA芯片技术,提出了全错位排列问题的基于芯片的DNA计算模型,并对模型进行了简要分析.     

Using Interval Analysis for Solving Planar Single-Facility Location Problems: New Discarding Tests

Interval analysis is a powerful tool which allows the design of branch-and-bound methods able to solve many global optimization problems. The key to the speed of those methods is the use of several tests to discard boxes or parts of boxes in which no optimal point may occur. In this paper we present three new discarding tests for two-dimensional problems which are specially suitable for planar single-facility location problems. The usefulness of the new tests is shown by a computational study.     

Multivariate irregular sampling theorem

In this paper,we prove a Marcinkiewicz-Zygmund type inequality for multivariate entire functions of exponential type with non-equidistant spaced sampling points. And from this result,we establish a multivariate irregular Whittaker-Kotelnikov-Shannon type sampling theorem.     

A Monte Carlo comparison of studentized bootstrap and permutation tests for heteroscedastic two-sample problems

The present Monte Carlo study compares bootstrap and permutation tests for semiparametric heteroscedastic two-sample testing problems of Behrens-Fisher type. The underlying functionals to be tested are (a) the difference of the means and (b) the Wilcoxon functionalP(Y < X) which is invariant under strictly increasing transformations. The consideration leads to semiparametric modifications of Welch type tests for the Behrens-Fisher model and an extended two-sample Wilcoxon test which also works under some null hypothesis with non-exchangeable distributions. The present Monte Carlo study confirms the high quality of studentized permutation tests at finite sample size. They are typically better than tests with asymptotic critical values and for many situations and they are also better than two-sample bootstrap tests when their type I error probabilities are compared.     

Goodness-of-Fit Tests for the Cauchy Distribution Based on the Empirical Characteristic Function

Let X ₁,...,X _n be independent observations on a random variable X. This paper considers a class of omnibus procedures for testing the hypothesis that the unknown distribution of X belongs to the family of Cauchy laws. The test statistics are weighted integrals of the squared modulus of the difference between the empirical characteristic function of the suitably standardized data and the characteristic function of the standard Cauchy distribution. A large-scale simulation study shows that the new tests compare favorably with the classical goodness-of-fit tests for the Cauchy distribution, based on the empirical distribution function. For small sample sizes and short-tailed alternatives, the uniformly most powerful invariant test of Cauchy versus normal beats all other tests under discussion.     

参数未知的多变量设置调整问题研究

针对存在起始设置偏差过程参数未知的多变量过程,考虑不同质量特性对总体的质量损失影响不同,研究了在调整费用恒定下的统计过程调整问题.基于过程的状态空间方程模型,利用贝叶斯方法对过程的未知参数和设置偏差进行估计,结合过程的费用结构给出了过程的调整策略.通过仿真与其他的调整策略进行了对比分析,仿真结果表明,提出的调整策略能够更为有效地减少过程的质量损失.     

基于矩阵初等变换的n元函数极值的快速判别法

给出了 n元函数极值的一个充分条件 ,并结合矩阵的初等变换建立了 n元函数极值的一种快速判别法 ,最后给出了一个例子     

联合检测过程位置参数和尺度参数的非参数Cusum控制图

用于检测生产过程的多数传统控制图都假定过程的受控分布是已知的,并假定数据服从正态分布。然而在很多情况下,由于没有足够的数据来估计过程的分布,这种假定就变得不现实,而非参数控制图却不需要任何关于分布的特殊形式的假定。另外,多数的已有控制图都是使用两个单独的均值与方差控制图来同时检测生产过程.本文中,我们提出一个新的基于Cramer-von-Mises(CvM)检验的非参数累积和控制图(称为CvM图)来同时检测过程位置参数和尺度参数。文中给出了基于不同受控平均运行长度(ARL)下的CvM图的控制限,通过步长的均值、方差及分位数来研究控制图的性能表现。最后用一个实例来说明CvM图的实际应用。     

Distributions Minimizing Fisher Information for Location in Kolmogorov Neighbourhoods

This paper is concerned with the problem of finding those distributionsminimizing Fisher information for location over Kolmogorov neighbourhoods ofdistribution functions G satisfying certain mild conditions. The case when Gis symmetric has been considered by quite a few authors. The general form ofthe solution is discussed. Furthermore we provide the solution of twoasymmetric distributions, namely, the extreme value distribution and thePearson's type IV distribution.     

Extreme Value Asymptotics for Multivariate Renewal Processes

For a sequence of partial sums ofd-dimensional independent identically distributed random vectors a corresponding multivariate renewal process is defined componentwise. Via strong invariance together with an extreme value limit theorem for Rayleigh processes, a number of weak asymptotic results are established for thed-dimensional renewal process. Similar theorems for the estimated version of this process are also derived. These results are suggested to serve as simultaneous asymptotic testing devices for detecting changes in the multivariate setting.     

Annealing Algorithms for Multisource Absolute Location Problems on Graph

A methodology is presented for applying annealing techniques tomultisource absolute location problems on graph. Two kinds ofobjective functions are considered: barycenters and centers. Aclass of new algorithms is described: its development startsfrom the iterative cluster-and-locate algorithm and reliesupon the relaxation of the integrality constraints onallocation variables. Experimental results are reported.     

Mean Location and Sample Mean Location on Manifolds: Asymptotics, Tests, Confidence Regions

In a previous investigation we studied some asymptotic properties of the sample mean location on submanifolds of Euclidean space. The sample mean location generalizes least squares statistics to smooth compact submanifolds of Euclidean space. In this paper these properties are put into use. Tests for hypotheses about mean location are constructed and confidence regions for mean location are indicated. We study the asymptotic distribution of the test statistic. The problem of comparing mean locations for two samples is analyzed. Special attention is paid to observations on Stiefel manifolds including the orthogonal groupO(p) and spheresS^k−1, and special orthogonal groupsSO(p). The results also are illustrated with our experience with simulations.     

Modeling and Exploring Multivariate Spatial Variation: A Test Procedure for Isotropy of Multivariate Spatial Data

In this paper an exploratory technique based on the diagonalization of cross-variogram matrices is described. Through the definition of a model for the analysis and simulation of multivariate spatial data, a test procedure for the assumption of isotropy of multivariate spatial data is proposed. Applications to simulated and real data are reported.     

指数分布危险函数的经验Bayes双侧检验的收敛速度: Ⅱ型截尾情形

本文讨论了Ⅱ型截尾情形下指数分布危险函数的经验Bayes (EB)双侧检验问题. 利用概率密度函数的核估计构造了经验Bayes检验函数, 在适当的条件下获得了它的收敛速度.     

Tests of fit for the Rayleigh distribution based on the empirical Laplace transform

In this paper a class of goodness-of-fit tests for the Rayleigh distribution is proposed. The tests are based on a weighted integral involving the empirical Laplace transform. The consistency of the tests as well as their asymptotic distribution under the null hypothesis are investigated. As the decay of the weight function tends to infinity the test statistics approach limit values. In a particular case the resulting limit statistic is related to the first nonzero component of Neyman’s smooth test for this distribution. The new tests are compared with other omnibus tests for the Rayleigh distribution.     

Importance Sampling for p-value Computations in Multivariate Tests

Abstract

An importance sampling procedure is developed to approximate the distribution of an arbitrary function of the eigenvalues for a matrix beta random matrix or a Wishart random matrix. The procedure is easily implemented and provides confidence intervals for the p-values of many of the commonly used test statistics in multivariate analysis. An adaptive procedure allows for the control of either absolute error or relative error in this p-value estimation through the choice of importance sample size.     

Empirical likelihood ratio tests for multivariate regression models

This paper proposes some diagnostic tools for checking the adequacy of multivariate regression models including classical regression and time series autoregression. In statistical inference, the empirical likelihood ratio method has been well known to be a powerful tool for constructing test and confidence region. For model checking, however, the naive empirical likelihood (EL) based tests are not of Wilks’ phenomenon. Hence, we make use of bias correction to construct the EL-based score tests and derive a nonparametric version of Wilks’ theorem. Moreover, by the advantages of both the EL and score test method, the EL-based score tests share many desirable features as follows: They are self-scale invariant and can detect the alternatives that converge to the null at rate n ^−1/2, the possibly fastest rate for lack-of-fit testing; they involve weight functions, which provides us with the flexibility to choose scores for improving power performance, especially under directional alternatives. Furthermore, when the alternatives are not directional, we construct asymptotically distribution-free maximin tests for a large class of possible alternatives. A simulation study is carried out and an application for a real dataset is analyzed.      

Multivariate nonparametric tests for independence

Multivariate generalizations of Bhuchongkul's bivariate rank statistics [Ann. Math. Statist.35 (1964)] have been introduced and studied in this paper for the purpose of testing mulitvariate independence. It is shown that the test statistics can be expressed as rank statistics which are easy to compute, have asymptotic normal distributions, and can detect mutual dependence in alternatives which are pairwise independent. The tests are compared to the Puri-Sen-Gokhale [[8]] tests and a normal theory test [ [1]] using Pitman efficiency.