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The prediction distribution for the heteroscedastic multivariate linear models

COMMUNICATIONS IN STATISTICS-THEORY AND METHODS 1999年第10期28卷 2477-2486页

作者： Kibria, BMG Univ British Columbia Dept Stat Vancouver BC V6T 1Z2 Canada

The heteroscedastic multivariate linear model with multivariate normal error distribution has been considered. Using the structural relation of the model, the prediction distribution of future responses of the model has been derived. It is observed that for known covariance parameters the prediction distribution of the model has a product of m multivariate Student t distribution. It is to be noted that the prediction distribution for the Student terror also has a product of m multivariate Student t distribution. Some special cases have been discussed.

关键词： double t multivariate linear model prediction distribution

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Variable selection in multivariate linear models with high-dimensional covariance matrix estimation

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JOURNAL OF multivariate ANALYSIS 2018年 166卷 78-97页

作者： Perrot-Dockes, Marie Levy-Leduc, Celine Sansonnet, Laure Chiquet, Julien Univ Paris Saclay UMR MIA Paris AgroParisTech INRA F-75005 Paris France

In this paper, we propose a novel variable selection approach in the framework of multivariate linear models taking into account the dependence that may exist between the responses. It consists in estimating beforehand the covariance matrix. of the responses and to plug this estimator in a Lasso criterion, in order to obtain a sparse estimator of the coefficient matrix. The properties of our approach are investigated both from a theoretical and a numerical point of view. More precisely, we give general conditions that the estimators of the covariance matrix and its inverse have to satisfy in order to recover the positions of the null and non null entries of the coefficient matrix when the size of Z is not fixed and can tend to infinity. We prove that these conditions are satisfied in the particular case of some Toeplitz matrices. Our approach is implemented in the R package MultiVarSel available from the Comprehensive R Archive Network (CRAN) and is very attractive since it benefits from a low computational load. We also assess the performance of our methodology using synthetic data and compare it with alternative approaches. Our numerical experiments show that including the estimation of the covariance matrix in the Lasso criterion dramatically improves the variable selection performance in many cases. (C) 2018 Elsevier Inc. All rights reserved.

关键词： High-dimensional covariance matrix estimation Lasso multivariate linear model Variable selection

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General multivariate linear modeling of surface shapes using SurfStat

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NEUROIMAGE 2010年第2期53卷 491-505页

作者： Chung, Moo K. Worsley, Keith J. Nacewicz, Brendon M. Dalton, Kim M. Davidson, Richard J. Univ Wisconsin Waisman Ctr Dept Biostat & Med Informat Madison WI 53705 USA Univ Wisconsin Waisman Lab Brain Imaging & Behav Madison WI 53705 USA Univ Wisconsin Dept Psychiat & Psychol Madison WI 53706 USA McGill Univ Dept Math & Stat Montreal PQ Canada Seoul Natl Univ Dept Brain & Cognit Sci Seoul 151 South Korea

Although there are many imaging studies on traditional ROI-based amygdala volumetry, there are very few studies on modeling amygdala shape variations This paper presents a unified computational and statistical framework for modeling amygdala shape variations in a clinical population The weighted spherical harmonic representation is used to parameterize, smooth out, and normalize amygdala surfaces The representation is subsequently used as an input for multivariate linear models accounting for nuisance covariates such as age and brain size difference using the SurfStat package that completely avoids the complexity of specifying design matrices. The methodology has been applied for quantifying abnormal local amygdala shape variations in 22 high functioning autistic subjects (C) 2010 Elsevier Inc All rights reserved

关键词： Amygdala Spherical harmonics Fourier analysis Surface flattening multivariate linear model SurfStat

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Visualizing hypothesis tests in multivariate linear models: the heplots package for R

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COMPUTATIONAL STATISTICS 2009年第2期24卷 233-246页

作者： Fox, John Friendly, Michael Monette, Georges McMaster Univ Dept Sociol Hamilton ON L8S 4M4 Canada York Univ Dept Psychol Toronto ON M3J 1P3 Canada York Univ Dept Math & Stat Toronto ON M3J 1P3 Canada

Hypothesis-error (or "HE") plots, introduced by Friendly (J Stat Softw 17(6):1-42, 2006a;J Comput Graph Stat 16:421-444, 2006b), permit the visualization of hypothesis tests in multivariate linear models by representing hypothesis and error matrices of sums of squares and cross-products as ellipses. This paper describes the implementation of these methods in the heplots package for R, as well as their extension, for example from two to three dimensions and by scaling hypothesis ellipses and ellipsoids in a natural manner relative to error.

关键词： multivariate linear model MANOVA linear hypotheses Data ellipses Statistical graphics

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A consistency property of the AIC for multivariate linear models when the dimension and the sample size are large

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ELECTRONIC JOURNAL OF STATISTICS 2015年第1期9卷 869-897页

作者： Yanagihara, Hirokazu Wakaki, Hirofumi Fujikoshi, Yasunori Hiroshima Univ Grad Sch Sci Dept Math Hiroshima 7398626 Japan

It is common knowledge that Akaike's information criterion (AIC) is not a consistent model selection criterion, and Bayesian information criterion (BIC) is. These have been confirmed from an asymptotic selection probability evaluated from a large-sample framework. However, when a high-dimensional asymptotic framework, such that the dimension of the response variables and the sample size are approaching oo, is used for evaluating the selection probability, there are cases that the AIC for selecting variables in multivariate linear models is consistent, but the BIC is not. The AIC and BIC are included in a family of information criteria defined by adding a penalty term expressing the complexity of the model to a negative twofold maximum log-likelihood. By clarifying the condition of the penalty term to ensure the consistency, we derive conditions for consistency of the AIC, BIC and other information criteria under the high-dimensional asymptotic framework.

关键词： AIC bias-corrected AIC BIC consistent AIC high-dimensional asymptotic framework multivariate linear model selection probability variable selection

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Quadratic prediction problems in multivariate linear models

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JOURNAL OF multivariate ANALYSIS 2009年第2期100卷 291-300页

作者： Liu, Xu-Qing Wang, Dong-Dong Rong, Jian-Ying Huaiyin Inst Technol Dept Comp Sci Huaian 223001 Peoples R China Huaian Coll Informat Technol Dept Fdn Courses Huaian 223003 Peoples R China

linear and quadratic prediction problems infinite populations have become of great interest to Many authors recently. In the present paper, we mainly aim to extend the problem Of quadratic prediction from a general linear model, of form y = X beta + e, e similar to N(0, sigma V-2), to a multivariate linear model, denoted by Y = XB + E. Vec(E) similar to N(0, Sigma circle times V) with Y = (Y-ij)(nxq) = (y(1),...., y(q)). Firstly, the optimal invariant quadratic unbiased (OIQU) predictor and the optimal invariant quadratic (potentially) biased (OIQB) predictor of Y'HY for any particular symmetric nonnegative definite matrix H satisfying HX = 0 are derived. Secondly, we consider predicting a'Y'HYb and tr(Y'HY).The corresponding restricted OIQU predictor and restricted OIQB predictor for them are given. In addition, we also offer four concluding remarks. One concerns the generalization of predicting a'Y'HYb and tr(Y'HY), and the others are concerned with three possible extensions from OlUltivariate linear models to growth curve models, to restricted multivariate linear models, and to matrix elliptical linear models. (C) 2008 Elsevier Inc. All rights reserved.

关键词： multivariate linear model (Restricted) OIQU/OIQB predictor Prediction MSE (matrix) Permutation matrix Unbiasedness Invariance Matrix elliptically contoured distribution

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All Admissible linear Estimators under Quadratic Loss in multivariate model

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Communications in Mathematical Research 2000年第1期000卷

作者： DENG Qi-rong CHEN Jian-bao Yunnan Normal University Yunnan University

For multivariate linear model Y=XΘ+ε, ～N(0,σ2∑(×)V), this paper is concerned with the admissibility of linear estimators of estimable function SXΘ in the class of ali estimators. All admissible linear estim... 详细信息

关键词： multivariate linear model quadratic loss admissible estimator

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General multivariate linear modeling of mandible surface using SurfStat 21

General multivariate linear modeling of mandible surface usi...

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21th Iranian Conference on Biomedical Engineering

作者： Abdolali, Fatemeh Zoroofi, Reza Aghaeizadeh Univ Tehran Sch Elect & Comp Engn Tehran Iran

ISBN: (纸本)9781479974184

We present a novel approach for modeling mandible shape variations in Temporomandibular Joint Osteoarthritis (TMJ OA) patients. We have employed weighted spherical harmonic (SPHARM) representation to parameterize and normalize mandible surfaces. This representation is fed to multivariate linear models which account for nuisance covariates such as age and mandible size. multivariate linear models are implemented using SurfStat package and using this implementation one can avoid the complexity of specifying design matrices. In several multivariate shape models, the Hotelling's T-square has been used as a test statistic. In Hotelling's T-square statistic, we can test the equality of vector means without considering redundant covariates. Thus we have used SurfStat package in which Hotelling's T-square framework is generalized to incorporate additional covariates. Our proposed methodology has been applied for investigating Mandibular condyle shape variations in 19 TMJ OA subjects. Promising results have been demonstrated in lesion localization which is an important step in surgical planning and treatment.

关键词： Temporomandibular joint Osteoarthritis Spherical Harmonics lesion detection multivariate linear model SurfStat

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Estimation of patterned covariance in the multivariate linear models: an outer product least-squares approach

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Statistics 2015年第2期49卷 p408-426页

作者： Liu, Xiaoqian Hu, Jianhua School of Statistics and Management Shanghai University of Finance and Economics and Key Laboratory of Mathematical Economics (SUFE) Ministry of Education Shanghai200433 People's Republic of China

In this article, we present a framework of estimating patterned covariance of interest in the multivariate linear models. The main idea in it is to estimate a patterned covariance by minimizing a trace distance function between outer product of residuals and its expected value. The proposed framework can provide us explicit estimators, called outer product least-squares estimators, for parameters in the patterned covariance of the multivariate linear model without or with restrictions on regression coefficients. The outer product least-squares estimators enjoy the desired properties in finite and large samples, including unbiasedness, invariance, consistency and asymptotic normality. We still apply the framework to three special situations where their patterned covariances are the uniform correlation, a generalized uniform correlation and a generalq-dependence structure, respectively. Simulation studies for three special cases illustrate that the proposed method is a competent alternative of the maximum likelihood method in finite size samples. [ABSTRACT FROM AUTHOR]

关键词： 62F12 62H12 estimation general q-dependence least squares multivariate linear model outer product least squares patterned covariance uniform correlation

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SELECTING AN ADAPTIVE SEQUENCE FOR COMPUTING RECURSIVE M-ESTIMATORS IN multivariate linear REGRESSION modelS

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Journal of Systems Science & Complexity 2013年第4期26卷 583-594页

作者： MIAO Baiqi TONG Qian WU Yuehua JIN Baisuo Department of Statistics and Finance University of Science and Technology of China Department of Mathematics and Statistics York UniversityTorontoOntarioM3J1P3Canada

In this paper, the authors consider an adaptive recursive algorithm by selecting an adaptive sequence for computing M-estimators in multivariate linear regression models. Its asymptotic property is investigated. The recursive algorithm given by Miao and Wu （1996） is modified accordingly. Simu- lation studies of the Mgorithm is also provided. In addition, the Newton-Raphson iterative algorithm is considered for the purpose of comparison.

关键词： Adaptive sequence M-estimation multivariate linear model recursive algorithm scatter parameters.

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