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Shrinkage priors for Bayesian estimation of the mean matrix in an elliptically contoured distribution

JOURNAL OF multivariate ANALYSIS 2010年第6期101卷 1483-1492页

作者： Tsukuma, Hisayuki Toho Univ Fac Med Ota Ku Tokyo 1438540 Japan

This paper deals with the problem of estimating the mean matrix in an elliptically contoured distribution with unknown scale matrix. The Laplace and inverse Laplace transforms of the density allow us not only to evaluate the risk function with respect to a quadratic loss but also to simplify expressions of Bayes estimators. Consequently, it is shown that generalized Bayes estimators against shrinkage priors dominate the unbiased estimator. (C) 2010 Elsevier Inc. All rights reserved.

关键词： Decision theory Hierarchical model The Laplace transformation Minimaxity multivariate linear model Quadratic loss Scale mixture Shrinkage estimator

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The general common Hermitian nonnegative-definite solution to the matrix equations AXA*=BB* and CXC*=DD* with applications in statistics

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JOURNAL OF multivariate ANALYSIS 2005年第2期93卷 257-266页

作者： Zhang, X Heilongjiang Univ Dept Math Harbin 150080 Peoples R China

We deduce a necessary and sufficient condition for the matrix equations AXA* = BB* and CXC* = DD* to have a common Hermitian nonnegative-definite solution, and a representation of the general common Hermitian nonnegative-definite solution to these two equations when they have such common solutions. Thereby, we solve a statistical problem which is concerned in testing linear hypotheses about regression coefficients in the multivariate linear model. This paper is a revision of Young et al. (J. multivariate Anal. 68 (1999) 165) whose mistake was pointed out in (linear Algebra Appl. 321 (2000) 123). (c) 2004 Elsevier Inc. All rights reserved.

关键词： Hermitian (symmetric) nonnegative-definite solution Hermitian (symmetric) positive-definite solution Matrix equation Kernel space Column space Moore-Penrose generalized inverse linear hypothesis multivariate linear model

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A Test for multivariate Analysis of Variance in High Dimension

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COMMUNICATIONS IN STATISTICS-THEORY AND METHODS 2012年第13-14期41卷 2602-2615页

作者： Yamada, Takayuki Srivastava, Muni S. Chuo Univ Grad Sch Sci & Engn Bunkyo Ku Tokyo 1128551 Japan Univ Toronto Dept Stat Toronto ON Canada

In this article, we consider the problem of testing a general multivariate linear hypothesis in a multivariate linear model when the N x 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). 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) test, or more appropriately Bai and Saranadasa (1996) test who gave its asymptotic version.

关键词： Asymptotic distribution MANOVA multivariate linear model Power comparison

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MAXIMUM-LIKELIHOOD-ESTIMATION OF A SET OF COVARIANCE MATRICES UNDER LOWNER ORDER RESTRICTIONS WITH APPLICATIONS TO BALANCED multivariate VARIANCE-COMPONENTS modelS

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ANNALS OF STATISTICS 1991年第2期19卷 850-869页

作者： CALVIN, JA DYKSTRA, RL

The problem of maximum likelihood estimation of Lowner ordered covariance matrices is considered. It is shown that a dual formulation of this problem is tractable and important in its own right. The interplay between the primal and dual problems suggests a general algorithm for computing the solutions to these problems. This algorithm has application to some estimation problems in balanced multivariate variance components models. The speed of convergence is also discussed for the variance components models.

关键词： ISOTONIC REGRESSION WISHART DENSITY FENCHEL DUALITY multivariate linear model RESTRICTED MAXIMUM LIKELIHOOD ESTIMATION REML VARIANCE COMPONENTS modelS LEAST SQUARES ESTIMATION

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Combining rule-based and embedding-based approaches to normalize textual entities with an ontology 11

Combining rule-based and embedding-based approaches to norma...

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11th International Conference on Language Resources and Evaluation (LREC)

作者： Ferre, Arnaud Deleger, Louise Zweigenbaum, Pierre Nedellec, Claire Univ Paris Saclay INRA MaIAGE F-78350 Jouy En Josas France Univ Paris Saclay CNRS LIMSI F-91405 Orsay France

ISBN: (纸本)9791095546009

In this paper, we propose a two-step method to normalize multi-word terms with concepts from a domain-specific ontology. Normalization is a critical step of information extraction. The method uses vector representations of terms computed with word embedding information and hierarchical information among ontology concepts. A training dataset and a first result dataset with high precision and low recall are generated by using the ToMap unsupervised normalization method. It is based on the similarities between the form of the term to normalize and the form of concept labels. Then, a projection of the space of terms towards the space of concepts is learned by globally minimizing the distances between vectors of terms and vectors of concepts. It applies multivariate linear regression using the previously generated training dataset. Finally, a distance calculation is carried out between the projections of term vectors and the concept vectors, providing a prediction of normalization by a concept for each term. This method was evaluated through the categorization task of bacterial habitats of BioNLP Shared Task 2016. Our results largely outperform all existing systems on this task, opening up very encouraging prospects.

关键词： ontology-based entity normalization vector-based model distributional semantics multivariate linear model

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A GENERAL-model FOR THE ANALYSIS OF MULTILEVEL DATA

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PSYCHOMETRIKA 1988年第4期53卷 455-467页

作者： GOLDSTEIN, H MCDONALD, RP MACQUARIE UNIV N RYDENSW 2113AUSTRALIA

A general model is developed for the analysis of multivariate multilevel data structures. Special cases of the model include repeated measures designs, multiple matrix samples, multilevel latent variable models, multi... 详细信息

关键词： complex surveys mixed effects models multivariate linear model repeated measures time series variance component models

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Joint fMRI brain activation detection and segmentation using Level Sets

Joint fMRI brain activation detection and segmentation using...

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32nd Annual International Conference of the IEEE Engineering-in-Medicine-and-Biology-Society (EMBC 10)

作者： Silveira, Margarida Figueiredo, Patricia Inst Super Tecn Inst Syst & Robot P-1049001 Lisbon Portugal

ISBN: (纸本)9781424441242

This paper proposes a parametric, multivariate method for the joint detection and segmentation of brain activation based on fMRI data. The proposed technique uses region based level sets to separate between the task-related and non-task-related regions and performs, at each iteration of level set evolution, a separate multivariate linear model (MLM) analysis in each of the two regions. Simulations using synthetic data generated based on typical experimental parameters and noise levels showed a false positive rate of 6% and a false negative rate of 2% for the results obtained with the proposed technique. The performance of the level sets method was further investigated by analysing empirical fMRI data from two subjects performing a visual and a motor task. Our results indicate that the proposed technique provides brain activation results comparable to those obtained by a standard univariate approach, with the advantage that it does not require the definition of a significance threshold.

关键词： biomedical MRI brain brain activation fMRI image segmentation image segmentation level sets method medical image processing motor task multivariate linear model visual task

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Advances on Dimension Reduction for multivariate linear Regression

Advances on Dimension Reduction for Multivariate Linear Regr...

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作者： Guo, Wenxing McMaster University

学位级别：博士

multivariate linear regression methods are widely used statistical tools in data analysis, and were developed when some response variables are studied simultaneously, in which our aim is to study the relationship between predictor variables and response variables through the regression coefficient matrix. The rapid improvements of information technology have brought us a large number of large-scale data, but also brought us great challenges in data processing. When dealing with high dimensional data, the classical least squares estimation is not applicable in multivariate linear regression analysis. In recent years, some approaches have been developed to deal with high-dimensional data problems, among which dimension reduction is one of the main approaches. In some literature, random projection methods were used to reduce dimension in large datasets. In Chapter 2, a new random projection method, with low-rank matrix approximation, is proposed to reduce the dimension of the parameter space in high-dimensional multivariate linear regression model. Some statistical properties of the proposed method are studied and explicit expressions are then derived for the accuracy loss of the method with Gaussian random projection and orthogonal random projection. These expressions are precise rather than being bounds up to constants. In multivariate regression analysis, reduced rank regression is also a dimension reduction method, which has become an important tool for achieving dimension reduction goals due to its simplicity, computational efficiency and good predictive performance. In practical situations, however, the performance of the reduced rank estimator is not satisfactory when the predictor variables are highly correlated or the ratio of signal to noise is small. To overcome this problem, in Chapter 3, we incorporate matrix projections into reduced rank regression method, and then develop reduced rank regression estimators based on random projection and orthogonal pro

关键词： Dimension reduction multivariate linear model Low rank matrix approximation Random projection Matrix projection Reduced rank regression High-dimensional data Group LASSO penalty Variable selection Sparsity Envelope model Multidimensional array Tensor regression Sparsity principle

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Admissibilty for Nonhomogeneous linear Estimates on multivariate Random Regression Coefficients and Parameters

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Chinese Quarterly Journal of Mathematics 1997年第3期12卷 63-70,页

作者：艾明要刘敬敏 Henan Institute

In this paper,we consider the admissibility for nonhomogeneous linear estimates on regression coefficients and parameters in multivariate random effect linear model and give eight definitions of different forms for admissibility. We not only prove that they can be divided into three identical subclasses,but also gain three kinds of necessary and sufficient conditions.

关键词： multivariate linear model random effect admissibility

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Robustní odhady v modelu CAPM

Robustní odhady v modelu CAPM

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作者： Steinhübelová, Monika Charles University of Prague

The thesis describes the theory of capital asset pricing model (CAPM) and the issue of robust estimates. Robust methods are an effective tool to achieve better estimation relative to the classical least squares method when there is a fai- lure to assume a normal distribution of errors or in the presence of outlying obser- vations in the data. Theory of M-estimates, which is then applied in the practical part of the thesis to the multidimensional CAPM model is treated in detail. The- ory of R- and L-estimates is explained in less detail. A simulation study compares simultaneous estimates in multivariate model and estimates designed individually when applied to the model assuming the mutual independence of equations. 1

关键词： robust estimates multivariate linear model CAPM model simultaneous estimates

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