Analyzing Mean Profiles of Nonnormal Populations

We consider testing whether the mean vectors of two or more populations have parallel, coincident, or flat profiles when the validity of normality is not known, and the sample sizes are moderate. Using some properties of multivariate moments and matrix manipulations, we obtain the asymptotic expansions for the null distribution of the Lawley–Hotelling statistics. We also derive the corresponding results in the situation where interest lies in coincidence and flatness alone. Accuracy of all the asymptotic expansions in approximating the exact null distributions is examined via simulation. Profile analysis of SO₄ concentrations from a forestry experiment is used to illustrate the methods.     

A mixture of the manova and gmanova models

A mixture of the MANOVA and GMANOVA models is presented. The expected value of the response matrix in this model is the sum of two matrix components. The first component represents the GMANOVA portion and the second component represents the MANOVA portion. Maximum likelihood estimators are derived for the parameters in this model, and goodness-of-fit tests are constructed for fuller models via the likelihood ration criterion. Finally, likelihood ration tests for general liinear hypotheses are developed and a numerical example is presented.     

A Test for Multivariate Analysis of Variance in High Dimension

In this article, we consider the problem of testing a general multivariate linear hypothesis in a multivariate linear model when the N × p observation matrix is normally distributed with unknown covariance matrix, and N ≤ p. This includes the case of testing the equality of several mean vectors. A test is proposed which is a generalized version of the two-sample test proposed by Srivastava and Du (2008 Srivastava , M. S. , Du , M. ( 2008 ). A test for the mean vector with fewer observations than the dimension . J. Multivariate Anal. 99 : 386 – 402 .[Crossref], [Web of Science ®] , [Google Scholar]). The asymptotic null and nonnull distributions are obtained. The performance of this test is compared, theoretically as well as numerically, with the corresponding generalized version of the two-sample Dempster (1958 Dempster , A. P. (1958). A high dimensional two sample significance test. Ann. Math. Statist. 29:995–1010.[Crossref] , [Google Scholar]) test, or more appropriately Bai and Saranadasa (1996 Bai , Z. , Saranadasa , H. ( 1996 ). Effect of high dimension: an example of a two sample problem . Statistica Sinica 6 : 311 – 329 .[Web of Science ®] , [Google Scholar]) test who gave its asymptotic version.     

Layered clays in PP polymer dispersion: the effect of the processing conditions

The effect of processing conditions of material and interfacial/ interphase properties in clay/polymer nanocomposites are usually studied through experimental results of X-ray diffraction, transmission electron microscopy and rheology mechanical tests. In this paper, the interaction of the experimental parameters and properties measure results are studied by employing multivariate analysis of variance technique. This model is used to establish relations between several material and interfacial/interphase characteristics with the processing conditions. These results are then analyzed in detail, using univariate approach (analysis of variance), to point out the existing significant relations. In general, agreement with experimental observations was found, but few other nonagreeable things are found out, which must be studied in the future. The effects of all parameters are thus determined, using these new approach, to predict the relations between material and interfacial/interphase properties, without the need to duplicate experiments in laboratory.     

新疆本科生英语学习动机调查

G ardner和L am bert认为学习动机主要有两大类:一是“工具型动机”,二是“融合型动机”。另一较为经典的语言学习动机模式是“内在动机”和“外在动机”。近年来,国内学者对动机的内在结构、动机与学习成绩的关系等方面也进行了相关研究。文章旨在探讨少数民族地区本科生的动机类型以及个人因素对动机类型的影响。研究工具是自编问卷L ikert-Sca le五级量表形式,进行因子分析及多元方差分析。     

国际电子商务研究中常用的感知风险分析方法

感知风险是国际电子商务研究中普遍关注的热点问题,也是消费者购买行为理论和模型的一个重要组成元素。通过国际主流感知风险研究的具体实例,介绍结构方程模型、模糊聚类分析、多变量方差分析等方法在国际电子商务中感知风险测量的实际应用,并对感知风险相关理论和方法应用于人机交互领域中的可行性进行探讨。     

Testing the equality of several multivariate normal mean vectors under heteroscedasticity: A fiducial approach and an approximate test

We consider the problem of testing the equality of several multivariate normal mean vectors under heteroscedasticity. We first construct a fiducial confidence region (FCR) for the differences between normal mean vectors and we then propose a fiducial test for comparing mean vectors by inverting the FCR. We also propose a simple approximate test that is based on a modification of the χ² approximation. This simple test avoids the complications of simulation-based inference methods. We show that the proposed fiducial test has correct type one error rate asymptotically. We compare the proposed fiducial and approximate tests with the parametric bootstrap test in terms of controlling the type one error rate via an extensive simulation study. Our simulation results show that the proposed fiducial and approximate tests control the type one error rate, while there are cases that the parametric bootstrap test is out of control. We also discuss the power performance of the tests. Finally, we illustrate with a real example how our proposed methods are applicable in analyzing repeated measure designs including a single grouping variable.     

Modelling interval data with Normal and Skew-Normal distributions

A parametric modelling for interval data is proposed, assuming a multivariate Normal or Skew-Normal distribution for the midpoints and log-ranges of the interval variables. The intrinsic nature of the interval variables leads to special structures of the variance–covariance matrix, which is represented by five different possible configurations. Maximum likelihood estimation for both models under all considered configurations is studied. The proposed modelling is then considered in the context of analysis of variance and multivariate analysis of variance testing. To access the behaviour of the proposed methodology, a simulation study is performed. The results show that, for medium or large sample sizes, tests have good power and their true significance level approaches nominal levels when the constraints assumed for the model are respected; however, for small samples, sizes close to nominal levels cannot be guaranteed. Applications to Chinese meteorological data in three different regions and to credit card usage variables for different card designations, illustrate the proposed methodology.     

Multivariate analysis of variance for functional data

Functional data are being observed frequently in many scientific fields, and therefore most of the standard statistical methods are being adapted for functional data. The multivariate analysis of variance problem for functional data is considered. It seems to be of practical interest similarly as the one-way analysis of variance for such data. For the MANOVA problem for multivariate functional data, we propose permutation tests based on a basis function representation and tests based on random projections. Their performance is examined in comprehensive simulation studies, which provide an idea of the size control and power of the tests and identify differences between them. The simulation experiments are based on artificial data and real labeled multivariate time series data found in the literature. The results suggest that the studied testing procedures can detect small differences between vectors of curves even with small sample sizes. Illustrative real data examples of the use of the proposed testing procedures in practice are also presented.     

Regularised Manova for High‐Dimensional Data

The traditional and readily available multivariate analysis of variance (MANOVA) tests such as Wilks' Lambda and the Pillai–Bartlett trace start to suffer from low power as the number of variables approaches the sample size. Moreover, when the number of variables exceeds the number of available observations, these statistics are not available for use. Ridge regularisation of the covariance matrix has been proposed to allow the use of MANOVA in high‐dimensional situations and to increase its power when the sample size approaches the number of variables. In this paper two forms of ridge regression are compared to each other and to a novel approach based on lasso regularisation, as well as to more traditional approaches based on principal components and the Moore‐Penrose generalised inverse. The performance of the different methods is explored via an extensive simulation study. All the regularised methods perform well; the best method varies across the different scenarios, with margins of victory being relatively modest. We examine a data set of soil compaction profiles at various positions relative to a ridgetop, and illustrate how our results can be used to inform the selection of a regularisation method.