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INFERENCE FOR REPEATED MEASURES MODELS UNDER HETEROSCEDASTICITY

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Journal of Systems Science & Complexity 2012年第6期25卷 1158-1170页

作者： Weiyan MU xingzhong xu Science School Beijing University of Civil Engineering and Architecture School of Mathematics Beijing Institute of Technology

This paper considers a widely used mixed effects model in repeated measures under het- eroscedasticity. Hypotheses of the equality of the fixed effects and the simultaneous confidence intervals for all pair-wise differences are discussed. A generalized F-test has been proposed to test the equality of the fixed effects in the model, but simulation results for evaluating its performance have not been shown in the literature. Moreover, the generalized F-test cannot be used to deduce the simultaneous confidence intervals for all pair-wise differences of the fixed effects. The authors propose two new p-values to test the hypotheses of equality of the fixed effects and simultaneous confidence intervals of the differences of the effects based on the generalized pivotal quantities derived in this paper. The authors also compare the empirical performances of the proposed tests and the generalized F-test. The type I error rates and powers of these tests are evaluated using the Monte Carlo simulation. The simulation studies show that the generalized F-test does not perform well in terms of type I error rate under various sample size and parameter combinations. However, the type I error probabilities of the proposed tests are always close to the nominal value. It can also be seen that the simultaneous confidence intervals perform well.

关键词： Generalized p-values heteroscedasticity mixed effect repeated measures models simul-taneous confidence intervals.

GENERALIZED CONFIDENCE REGIONS OF FIXED EFFECTS IN THE TWO-WAY ANOVA

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Journal of Systems Science & Complexity 2008年第2期21卷 276-282页

作者： Weiyan MU Shifeng XIONG xingzhong xu Department of Mathematics Beijing Institute of Technology Beijing 100081 China Academy of Mathematics and Systems Science Chinese Academy of Sciences Beijing 100190 China

The authors discuss the unbalanced two-way ANOVA model under heteroscedasticity. By taking the generalized approach, the authors derive the generalized p-values for testing the equality of fixed effects and the generalized confidence regions for these effects. The authors also provide their frequentist properties in large-sample cases. Simulation studies show that the generalized confidence regions have good coverage probabilities.

关键词： ANOVA generalized confidence region generalized p-value heteroscedasticity unbalanced.

A NEW PROCEDURE FOR TESTING NORMALITY BASED ON THE L_2 WASSERSTEIN DISTANCE

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Journal of Systems Science & Complexity 2013年第4期26卷 572-582页

作者： HE Daojiang xu xingzhong ZHAO Jianxin School of Mathematics Beijing Institute of Technology Department of Statistics Anhui Normal University Navy Submarine Academy

This paper proposes a new goodness-of-fit test for normality based on the L~ Wasserstein distance. The authors first construct a probability through the Bootstrap resampling. Although the probability is not distributed uniformly on the interval （0, 1） under the null hypothesis, it is shown that its distribution is free from the unknown parameters, which indicates that such a probability can be taken as the test statistic. It emerges from the simulation study of power that the new test is able to better discriminate between the normal distribution and those distributions with short tails. For such alternatives, it has a substantially better power than existing tests including the Anderson-Darling test and Shapiro-Wilk test, which are two of the best tests for normality. In addition, the sensitivity analysis of tests is also investigated in the presence of moderate perturbation, which shows that the new test is a rather robust test.

关键词： Anderson-Darling test goodness-of-fit test Shapiro-Wilk test Wasserstein distance.

GENERALIZED p-VALUES FOR TESTING REGRESSION COEFFICIENTS IN PARTIALLY LINEAR MODELS

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Journal of Systems Science & Complexity 2010年第6期23卷 1118-1132页

作者： Huimin HU xingzhong xu Guoying LI School of Statistics and Mathematics Shandong University of Finance Jinan 250014 China. Department of Mathematics Beijing Institute of Technology Beijing 100081 China. Academy of Mathematics and Systems Science Chinese Academy of Sciences Beijing 100190 China.

The one-sided and two-sided hypotheses about the parametric component in partially linear model are considered in this paper. Generalized p-values are proposed based on fiducial method for testing the two hypotheses at the presence of nonparametric nuisance parameter. Note that the nonparametric component can be approximated by a linear combination of some known functions, thus, the partially linear model can be approximated by a linear model. Thereby, generalized p-values for a linear model are studied first, and then the results are extended to the situation of partially linear model. Small sample frequency properties are analyzed theoretically. Meanwhile, simulations are conducted to assess the finite sample performance of the tests based on the proposed p-values.

关键词： Fiducial inference frequency property generalized p-value hypothesis testing partially linear model.

Statistical inference on mixing proportion

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Science China Mathematics 2008年第9期51卷 1593-1608页

作者： xu xingzhong LIU Fang Department of Mathematics Beijing Institute of TechnologyBeijing 100081China The People’s Insurance Company(Group)of China Beijing 100084China

In this paper, the interval estimation and hypothesis testing of the mixing proportion in mixture distributions are considered. A statistical inferential method is proposed which is inspired by the generalized p-values and generalized pivotal quantity. In some situations, the true levels of the tests given in the paper are equal to nominal levels, and the true coverage of the interval estimation or confidence bounds is also equal to nominal one. In other situations, under mild conditions, the tests are consistent and the coverage of the interval estimations or the confidence bounds is asymptotically equal to nominal coverage. Meanwhile, some simulations are performed which show that our method is satisfactory.

关键词： asymptotic properties generalized pivotal quantity generalized p value mixing proportion mixture distributions 62F03

On the Residual Finiteness of a Class of Infinite Soluble Groups

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Algebra Colloquium 2023年第1期30卷 155-164页

作者： Jun Liao Heguo Liu Xiaoliang Luo xingzhong xu School of Mathematics and Statistics Hubei UniversityWuhan 430062China Department of Mathematics Hainan UniversityHaikou 570228China Department of Mathematics Taiyuan Normal University JinzhongShanxi 031609China

Let A be a completely decomposable homogeneous torsion-free abelian group of rank n(n≥2).Let m(n)=A×(a)be the split extension of A by an automorphismαwhich is a cyclic permutation of the direct components twisted b... 详细信息

关键词： residual finiteness infinite soluble group nilpotent group polycyclic group

Preparation of MCM-41 in Industrial Scale and Its Application in Heavy Oil Processing

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Chemical Research in Chinese Universities 2002年第2期18卷 169-174页

作者： Jianwen Da Tiancun Xiao Jianming Su xingzhong xu Malcolm L.H.Green Research Institute of Qilu Petrochem.Corp. Zibo 255400China The Wolfson Catalysis Centre Inorganic Chemistry LaboratoryUniversity of OxfordSouth Parks RoadOxfordOX13QRUK

A series of MCM 41 molecular sieves have been prepared on an industrial scale, and the effect of preparation factors such as aging temperature, pH values on the structure and pore distribution of the MCM 41 product have been studied by using X ray diffraction(XRD), thermogravimetric(TG) and electron microscopy(TEM). It is shown that the pH values have a significant effect on the crystallinity of the synthesized product. Under proper conditions, the MCM 41 prepared on an industrial scale has the same performance as the samples prepared on an Lab scale. The prepared MCM 41 was used as a modifier of zeolite Y for fluid catalytic cracking(FCC) of residual oil. It is shown that the addition of the MCM 41 in the zeolite Y catalyst increases the pore size, and surface area of the catalysts, which helps to increase the yield of gasoline and diesel and decrease the production of gaseous product and carbon deposition in the catalyst. The better performance of the MCM 41 modified zeolite Y catalyst is believed to be due to its adjustment on the acidity and increase of the pore size.

关键词： MCM-41 Industrial scale synthesis FCC catalyst

Local canonical correlation coefficients and canonical variables of groups of random variables

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Chinese Science Bulletin 1998年第10期43卷 815-817页

作者： xu xingzhong Institute of Systems Science, Chinese Academy of Sciences, Beijing 100080, China Institute of Systems Science Chinese Academy of Sciences Beijing China

The concepts of local correlation coefficient, local canonical correlation coefficients and local canonical variables of groups of random variables are defined, which generalize the classical concepts in two groups of random *** concepts together with total corresponding concepts clarify the correlativity among groups of random variables.

关键词： groups of random variables covariance matrix local canonical correlation coefficients local canonical variables.

Fiducial inference in the pivotal family of distributions

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Science China Mathematics 2006年第3期49卷 410-432页

作者： xu xingzhong & LI Guoying Department of Mathematics, Beijing Institute of Technology, Beijing 100081, China Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing 100080, China 1. Department of Mathematics Beijing Institute of Technology Beijing 100081 China 2. Academy of Mathematics and Systems Science Chinese Academy of Sciences Beijing 100080 China

In this paper a family, called the pivotal family, of distributions is considered.A pivotal family is determined by a generalized pivotal model. Analytical results show that a great many parametric families of distributions are pivotal. In a pivotal family of distributions a general method of deriving fiducial distributions of parameters is proposed. In the method a fiducial model plays an important role. A fiducial model is a function of a random variable with a known distribution, called the pivotal random element, when the observation of a statistic is *** method of this paper includes some other methods of deriving fiducial distributions. Specially the first fiducial distribution given by Fisher can be derived by the method. For the monotone likelihood ratio family of distributions, which is a pivotal family, the fiducial distributions have a frequentist property in the Neyman-Pearson view. Fiducial distributions of regular parametric functions also have the above frequentist property. Some advantages of the fiducial inference are exhibited in four applications of the fiducial distribution. Many examples are given, in which the fiducial distributions cannot be derived by the existing methods.

关键词： confidence bounds, fiducial distributions, fiducial model, frequentist prop-erty, generalized pivotal model, pivotal family of distributions, testing hypotheses.