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Testing homogeneity of mean vectors under heteroscedasticity in high-dimension

Takayuki Yamada, Tetsuto Himeno
2015 Journal of Multivariate Analysis  
This paper is concerned with the problem of testing the homogeneity of mean vectors. The testing problem is without assuming common covariance matrix.  ...  It is found that our proposed test has the same limiting power as the one of Dempster's trace statistic for MANOVA proposed in Fujikoshi, Himeno and Wakaki (2004, JJSS) for the case that the population  ...  Concluding remarks This article is considered to test the homogeneity of mean vectors under heteroscedasticity for some groups.  ... 
doi:10.1016/j.jmva.2015.02.005 fatcat:iumjo7oruffmnbljoth6fsdz7y

Empirical Likelihood Ratio Tests for Coefficients in High Dimensional Heteroscedastic Linear Models

Honglang Wang, Ping-Shou Zhong, Yuehua Cui
2018 Statistica sinica  
This paper considers hypothesis testing problems for a low-dimensional coefficient vector in a high-dimensional linear model with heteroscedastic variance.  ...  The proposed method is able to make valid inference even when the conditional variance of random error is an unknown function of high-dimensional predictors.  ...  Supplemental material In this supplemental file, we provide technical proofs to all the theoretical results presented in the paper, and some additional simulation results.  ... 
doi:10.5705/ss.202017.0041 fatcat:4q2pvjaacrc7fawmiahhjzn5fq

A Statistical Analysis of Brain Morphology Using Wild Bootstrapping

Hongtu Zhu, J.G. Ibrahim, Niansheng Tang, D.B. Rowe, Xuejun Hao, R. Bansal, B.S. Peterson
2007 IEEE Transactions on Medical Imaging  
under investigation.  ...  We demonstrate the application of this robust test procedure to the detection of statistically significant differences in the morphology of the hippocampus over time across gender groups in a large sample  ...  characteristic density of the field in dimension.  ... 
doi:10.1109/tmi.2007.897396 pmid:17649909 pmcid:PMC2367010 fatcat:my5q25lzcnha3l5k4e447aj6om

envlp: AMATLABToolbox for Computing Envelope Estimators in Multivariate Analysis

Dennis Cook, Zhihua Su, Yi Yang
2014 Journal of Statistical Software  
The envlp toolbox implements a variety of envelope estimators under the framework of multivariate linear regression, including the envelope model, partial envelope model, heteroscedastic envelope model  ...  errors, F test for two nested models, the standard errors for contrasts or linear combinations of coefficients, and more.  ...  To test homogeneity of the covariance matrices, Box's M test (Johnson and Wichern 2007) can be used.  ... 
doi:10.18637/jss.v062.i08 fatcat:2nplbrzdrvgy7nqi4bjizeexiy

A Modified Bartlett Test for Heteroscedastic Two-way MANOVA

Jin-Ting Zhang, Bu Zhou, Jia Guo, Xuefeng Liu
2016 Journal of Advanced Statistics  
Simulation studies show that the MB test generally outperforms the classical Lawley-Hotelling trace (LHT) test and a modified LHT test of [3] under various parameter configurations in terms of size controlling  ...  In this paper, we propose and study a Modified Bartlett (MB) test using a Wald-type statistic and the modified Bartlett correction ([2]) for heteroscedastic two-way MANOVA problems.  ...  In terms of power, the MB test outperforms the LHT m test for almost all the cases except for some homogeneous cases under the N (0, 1) scheme.  ... 
doi:10.22606/jas.2016.12006 fatcat:i5f55gdwcrgd7l3plc5geihsxy

Modeling Panel Data: Comparison of GLS Estimation and Robust Covariance Matrix Estimation

Victor Muthama Musau
2015 American Journal of Theoretical and Applied Statistics  
Much controversy on these methodologies is the under-estimation of the standard errors leading to wrong conclusions of the involved hypothesis test as well as making inappropriate inference to the underlying  ...  This is due to the heteroscedasticity and autocorrelation nature of the disturbance term in the classical linear regression model.  ...  of the homogenous hypothesis.  ... 
doi:10.11648/j.ajtas.20150403.25 fatcat:hbf2rxglznfofacgfapthdspve

Modified Tests for Heteroscedastic Two-Way MANOVA

Shengning Xiao, Jin-Ting Zhang
2016 Journal of Advanced Statistics  
of the cell mean vectors.  ...  In this article we consider testing for main and interaction effects in heteroscedastic two-way MANOVA model.  ...  Note that M is a matrix of size (ab) × p whose rows are the ab cell mean vectors. Denote an l-dimensional unit vector whose rth component is 1 and others are 0 as e r,l .  ... 
doi:10.22606/jas.2016.11001 fatcat:gfeyypfblzgztgjg656g3z7le4

Random Utility-Based Discrete Choice Models for Travel Demand Analysis [chapter]

Chandra Bhat
2002 New Directions in Civil Engineering  
{0,1} S and consider any S-dimensional uniformly distributed vector in the S-dimensional cube (u ?{0,1} S ). is a matrix of dimension N x S, and u is a vector of dimension 1xS.  ...  a vector of observed data associated with alternative i, some of whose elements might also appear in the vector is a random vector with zero mean.  ... 
doi:10.1201/9781420042283.ch10 fatcat:upizd3p24vhgzo2h55cnqeh3xi

Heterogeneous variances and genetics by environment interactions in genetic evaluation of crossbred lambs

G. C. Márquez, W. Haresign, M. H. Davies, R. Roehe, L. Bünger, G. Simm, R. M. Lewis
2014 Animal  
In conclusion, heteroscedasticity and G×E were not large for these data, and can be ignored in genetic evaluation of weight but, perhaps, not ultrasonic traits.  ...  The objectives of this study were to evaluate the presence and consequences of heteroscedasticity and G×E on genetic evaluation.  ...  In progeny testing of dairy cattle, ranking of bulls was not greatly affected by heteroscedasticity when their daughters were randomly distributed among farms with high and low variances (Winkelman and  ... 
doi:10.1017/s1751731114002717 pmid:25407759 fatcat:3mwc2opbxjeefjhjft5fbzlo5i

Estimation of multivariate means with heteroscedastic errors using envelope models

Zhihua Su, R. Dennis Cook
2012 Statistica sinica  
In this article, we propose envelope models that accommodate heteroscedastic error structure in the framework of estimating multivariate means for different populations.  ...  In the original development, constant covariance structure is assumed. The heteroscedastic envelope models we proposed are more flexible in allowing a more general covariance structure.  ...  Acknowledgment The work is supported in part by a Doctoral Dissertation Fellowship from the Graduate School, University of Minnesota, and by National Science Foundation Grant DMS-1007547.  ... 
doi:10.5705/ss.2010.240 fatcat:z4du3vhhuzcz3cafycllmukz3e

Among-environment heteroscedasticity and genetic autocorrelation: implications for the study of phenotypic plasticity

P Dutilleul, C Potvin
1995 Genetics  
In a multivariate analysis-of-variance model, three transformations of genotypic profiles (reaction norms), which apply to the residuals of the model while preserving the mean responses within environments  ...  When both nuisances are not removed, statistical tests are corrected in a modified univariate approach using the sample covariance matrix of the genotypic profiles.  ...  The authors are indebted to GRAHAM BELL for permission to reanalyze his data in the present paper and for motivating discussions and reading of a first draft.  ... 
pmid:7789780 pmcid:PMC1206505 fatcat:3i5l6aavdrfkvbjgzbglvfhtzu

Among-environment heteroscedasticity and genetic autocorrelation: implications for the study of phenotypic plasticity

P Dutilleul, C Potvin
1995 Genetics  
In a multivariate analysis-of-variance model, three transformations of genotypic profiles (reaction norms), which apply to the residuals of the model while preserving the mean responses within environments  ...  When both nuisances are not removed, statistical tests are corrected in a modified univariate approach using the sample covariance matrix of the genotypic profiles.  ...  The authors are indebted to GRAHAM BELL for permission to reanalyze his data in the present paper and for motivating discussions and reading of a first draft.  ... 
doi:10.1093/genetics/139.4.1815 fatcat:cix73r3ujjaxtbbxhl6nwqqszi

Uncertainty Bounds for Multivariate Machine Learning Predictions on High-Strain Brittle Fracture [article]

Cristina Garcia-Cardona, M. Giselle Fernández-Godino, Daniel O'Malley, Tanmoy Bhattacharya
2021 arXiv   pre-print
Simulation of the crack network evolution on high strain rate impact experiments performed in brittle materials is very compute-intensive.  ...  In this work, we extend the heteroscedastic uncertainty estimates to bound a multiple output machine learning emulator.  ...  Acknowledgements The authors are grateful to the anonymous reviewers, whose comments and suggestions helped improve the clarity of the manuscript.  ... 
arXiv:2012.15739v2 fatcat:md2hu4ejjnhcbf4nbbax3rx34m

MANOVA for Nested Designs with Unequal Cell Sizes and Unequal Cell Covariance Matrices

Li-Wen Xu
2014 Journal of Applied Mathematics  
For the heteroscedastic cases, the PB test outperforms the AHT test in terms of power. In addition, the PB test does not lose too much power when the homogeneity assumption is actually valid.  ...  For the problem of testing "main effects" of both factors, we develop a flexible test based on a parametric bootstrap approach. The PB test is shown to be invariant under affine-transformations.  ...  Acknowledgments This work was supported by the National Natural Science Foundation of China (11171002) and the Importation and Development of High-Caliber Talents Project of Beijing Municipal Institutions  ... 
doi:10.1155/2014/649202 fatcat:42zjbz6zujdgtbgzkcdhmx3d5y

Profiling heteroscedasticity in linear regression models

Qian M. Zhou, Peter X.-K. Song, Mary E. Thompson
2015 Canadian journal of statistics  
This proposed method is generalized to accommodate practical complications, such as when covariates associated with the heteroscedastic variances might not be associated with the mean structure of the  ...  Diagnostics for heteroscedasticity in linear regression models have been intensively investigated in the literature.  ...  The authors also thank the two anonymous referees, the AE and Editor for their valuable comments that have led to an improvement in the theory and application presented in the paper.  ... 
doi:10.1002/cjs.11252 fatcat:tlqi6okaoffgtalpkig4bejj7y
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