A bootstrap goodness of fit test for the generalized Pareto distribution

This paper proposes a bootstrap goodness of fit test for the Generalized Pareto distribution (GPd) with shape parameter γ. The proposed test is an intersection–union test which tests separately the cases of γ≥0 and γ<0 and rejects if both cases are rejected. If the test does not reject, then it is known whether the shape parameter γ is either positive or negative. A Monte Carlo simulation experiment was conducted to assess the power of performance of the intersection–union test. The GPd hypothesis was tested on a data set containing Mexico City’s ozone levels. ¹     

A maximum entropy type test of fit

In this paper, we propose a test of fit based on maximum entropy. The asymptotic distribution of the proposed test statistic is established and a corrected form for small and medium sample sizes is furnished. The performance of the test is investigated through extensive Monte Carlo simulations. Real examples are also presented and analyzed.     

基于卡方拟合优度检验的序列等概性测试组

等概性是随机性中的一个重要特性,频数检验是最常见的等概性检验方法.分析了传统频数检验的片面性,利用卡方拟合优度检验提出了全面进行等概性检验的测试组,分别是码元频数检验、等长子序列频数检验和检验结果数据频数检验.使用测试组对国际上常用的随机样本的二进制展开序列进行检验,实验结果表明,该测试组具有较强的等概性检验能力.     

Goodness of fit tests via exponential series density estimation

The properties of a new nonparametric goodness of fit test are explored. It is based on a likelihood ratio test, applied via a consistent series density estimator in the exponential family. The focus is on its computational and numerical properties. Specifically it is found that the choice of approximating basis is not crucial and that the choice of model dimension, through data-driven selection criteria, yields a feasible, parsimonious procedure. Numerical experiments show that the new tests have significantly more power than established tests, whether based upon the empirical distribution function, or alternate density estimators.     

CHITEST: A Monte-Carlo computer program for contingency table tests

CHITEST is an interactive FORTRAN 77 program that uses Monte-Carlo methods to test the null hypothesis that the row and column factors of a r-by-k contingency table are independent of each other. The program optionally performs the test for two populations: (1) the population of tables that have the same row and column marginal frequencies as the observed table; and (2) the population of tables that have the same total frequency as the observed table. The test does not require the expected cell frequencies to be large values—a requirement necessary for the standard chi-square test of independence to be valid. The program also will test the goodness-of-fit of an empirical distribution to a discrete theoretical distribution, and this test does not require large expected values for the theoretical distribution.     

A new algorithm based on copulas for VaR valuation with empirical calculations

This paper concerns the application of copula functions in VaR valuation. The copula function is used to model the dependence structure of multivariate assets. After the introduction of the traditional Monte Carlo simulation method and the pure copula method we present a new algorithm based on mixture copula functions and the dependence measure, Spearman’s rho. This new method is used to simulate daily returns of two stock market indices in China, Shanghai Stock Composite Index and Shenzhen Stock Composite Index, and then empirically calculate six risk measures including VaR and conditional VaR. The results are compared with those derived from the traditional Monte Carlo method and the pure copula method. From the comparison we show that the dependence structure between asset returns plays a more important role in valuating risk measures comparing with the form of marginal distributions.     

Approximating the distribution of goodness of fit tests for discrete data

The Berry-Esseen theorem is used to study the error of the normal approximation to the distribution of several goodness of fit tests for discrete data. A practical bound is proposed and confirmed by simulations.     

A goodness of fit test for the Pareto distribution in the presence of Type II censoring, based on the cumulative hazard function

A goodness of fit test for the Pareto distribution, when the observations are subjected to Type II right censoring is proposed. The test statistic involves transformations of the original data and is based on the nonparametric Nelson-Aalen estimator of the cumulative hazard function. By Monte Carlo simulation, the empirical distribution of the test statistic is obtained and the power of the test is investigated for some alternative distributions. The power is compared with adaptations for Type II censored data of the Crámer-von Mises and Anderson-Darling tests, and a test based on Kullback-Leibler information. For some alternative distributions with monotone decreasing hazard function, the proposed test has higher power. The methodology is illustrated by reanalyzing two published data sets.     

Robust estimators and tests for bivariate copulas based on likelihood depth

Estimators and tests based on likelihood depth for one-parametric copulas are given. For the Gaussian and Gumbel copulas, it is shown that the maximum depth estimators are biased. They can be corrected and the new estimators are robust against contamination. For testing, simplicial likelihood depth is considered. Because of the bias of the maximum depth estimator, simplicial likelihood depth is not a degenerated U-statistic so that easily asymptotic α-level tests can be derived for arbitrary hypotheses. Tests are in particular investigated for the one-sided alternatives. Simulation studies for the Gaussian and Gumbel copulas show that the power of the first test is rather good, but the latter one has to be improved, which is also done here. The new tests are robust against contamination.     

The random projection method in goodness of fit for functional data

The possibility of considering random projections to identify probability distributions belonging to parametric families is explored. The results are based on considerations involving invariance properties of the family of distributions as well as on the random way of choosing the projections. In particular, it is shown that if a one-dimensional (suitably) randomly chosen projection is Gaussian, then the distribution is Gaussian. In order to show the applicability of the methodology some goodness-of-fit tests based on these ideas are designed. These tests are computationally feasible through the bootstrap setup, even in the functional framework. Simulations providing power comparisons of these projections-based tests with other available tests of normality, as well as to test the Black-Scholes model for a stochastic process are presented.     

QFT template generation for time-delay plants based on zero-inclusion test

Plant template generation is the key step in applying quantitative feedback theory (QFT) to design robust control for uncertain systems. In this paper we propose a technique for generating plant templates for a class of linear systems with an uncertain time delay and affine parameter perturbations in coefficients. The main contribution lies in presenting a necessary and sufficient condition for the zero inclusion of the value set f(T,Q)={f(τ,q): τT[τ⁻,τ⁺], qQ∏_k=0^m−1[q_k⁻,q_k⁺]}, where f(τ,q)=g(q)+h(q)e^−jτω*, g(q) and h(q) are both complex-valued affine functions of the m-dimensional real vector q, and ω^* is a fixed frequency. Based on this condition, an efficient algorithm which involves, in the worst case, evaluation of m algebraic inequalities and solution of m2^m−1 one-variable quadratic equations, is developed for testing the zero inclusion of the value set f(T,Q). This zero-inclusion test algorithm allows one to utilize a pivoting procedure to generate the outer boundary of a plant template with a prescribed accuracy or resolution. The proposed template generation technique has a linear computational complexity in resolution and is, therefore, more efficient than the parameter gridding and interval methods. A numerical example illustrating the proposed technique and its computational superiority over the interval method is included.     

A new approach of goodness-of-fit testing for exponentiated laws applied to the generalized Rayleigh distribution

Goodness-of-fit statistics are considered which are appropriate for generalized families of distributions, resulting from exponentiation. The tests employ a variation of the data determined by the cumulative distribution function of the corresponding non-generalized distribution. The resulting test, which makes use of the Mellin transform of the transformed data, is shown to be consistent. Simulation results for the case of the generalized Rayleigh distribution show that the proposed test compares well with standard methods based on the empirical distribution function.     

基于可配置规则的BOM视图转换方法

在确保物料清单(bill of material,BOM)多视图之间产品数据一致性和完整性的前提下,为实现BOM视图转换技术能够满足企业业务规则的个性化需求并适应企业业务规则可能发生的改变,提出了基于可配置规则的BOM视图转换方法.在分析企业中各种BOM视图之间关系的基础上,建立了BOM视图及其转换过程的基础模型,给出了装配转换规则的结构定义及其配置方法,通过实际案例介绍了该方法在BOM视图转换过程中的应用,表明了该方法能够满足企业业务规则的个性化需求并适应企业业务规则的变化.     

一种基于小波的图像降噪方法

通过对图像的小波变换系数进行阈值操作,可有效降低噪声,但还是保留一些噪声。Wiener滤波是一种线性滤波方法,用小波阈值方法结合Wiener滤波,可进一步对图像噪声进行降噪。实验结果表明小波阈值Wiener滤波方法是一种有效的图像降噪方法,其在图像恢复上和人眼视觉上都优于小波阈值方法。     

Comparison of several means: A fiducial based approach

To study the equality of several normal means when the variances are unknown and unequal, we propose a fiducial based test, and theoretically examine the frequentist property of the proposed test. We numerically compare the performance of the proposed approach with several tests, recently developed such as the generalized F-test by Weerahandi (1995a), the trimmed mean-based test by Lix and Keselman (1998), and the parametric bootstrap test by Krishnamoorthy et al. (2007). The simulation results indicate that the proposed approach can provide a reasonable p-value via a few straightforward simulation steps. Finally, the proposed approach is applied to an analysis of two real data sets for illustration.     

基于矩阵变换的彩色图像加密算法

研究了矩阵变换的性质,找到一种新的SCAN遍历矩阵,对彩色图像各分量进行像素位置置乱,结合彩色图像结构特点,利用彩色图像每个像素的RGB分量构成三维列向量,并将其作为输入分量,经过矩阵变换,改变其像素值的大小,得到加密矩阵.试验结果表明,加密图像具有类随机性,直方图接近于均匀分布,算法具有很强的密钥敏感性.     

基于高帽变换预处理的OTSU分割算法

Otsu分割算法是阈值分割技术中广泛使用的一类方法,但它不能准确分割对比度较低或变化较大的图像.借助于数学形态学中高帽变换的概念,提出了一种改进的Otsu算法:先用高帽变换对原始图像处理,在处理后的图像上再进行Otsu分割.仿真实验表明,该方法具有较低的算法复杂度,容易实现且能成功分割出Otsu法不能分割的对象,比Ot...     

基于API测试的分布式测试框架的研究与实现

以APT测试为应用背景,在研究现有的测试驱动器的基础上设计了一个较完整的分布式测试框架,同时对一些关键技术的实现进行了讨论。该分布式测试框架采用客户机／服务器模型和对称结构,可以应用于分布式测试口远程测试及非分布式测试,具有自动化测试能力,同时考虑了对第3方测试工具的松散集成。     

A singular loop transformation framework based on non-singular matrices

In this paper, we discuss a loop transformation framework that is based on integer non-singular matrices. The transformations included in this framework are called Λ-transformations and include permutation, skewing and reversal, as well as a transformation calledloop scaling. This framework is more general than existing ones; however, it is also more difficult to generate code in our framework. This paper shows how integer lattice theory can be used to generate efficient code. An added advantage of our framework over existing ones is that there is a simple completion algorithm which, given a partial transformation matrix, produces a full transformation matrix that satisfies all dependences. This completion procedure has applications in parallelization and in the generation of code for NUMA machines. This work was supported by the Cornell Theory Center, NSF Presidential Young Investigator award #CCR-8958543. by NSF Grant #CCR-9008526, and by a grant from the Hewlett-Packard Company.