MATS: Inference for potentially singular and heteroscedastic MANOVA

JOURNAL OF MULTIVARIATE ANALYSIS

卷:165

Article

Friedrich, Sarah¹  Pauly, Markus¹ 

[1] Univ Ulm, Inst Stat, Ulm, Germany

关键词: Confidence regions;    Multivariate data;    Parametric bootstrap;    Singular covariance matrices;   

DOI  :  10.1016/j.jmva.2017.12.008

来源: Elsevier

【 摘 要 】

In many experiments in the life sciences, several endpoints are recorded per subject. The analysis of such multivariate data is usually based on MANOVA models assuming multivariate normality and covariance homogeneity. These assumptions, however, are often not met in practice. Furthermore, test statistics should be invariant under scale transformations of the data, since the endpoints may be measured on different scales. In the context of high-dimensional data, Srivastava and Kubokawa (2013) proposed such a test statistic for a specific one-way model; however, it relies on the assumption of a common non-singular covariance matrix. We modify and extend this test statistic to factorial MANOVA designs, incorporating general heteroscedastic models. In particular, our only distributional assumption is the existence of the group-wise covariance matrices, which may even be singular. We base inference on quantiles of resampling distributions, and derive confidence regions and ellipsoids based on these quantiles. In a simulation study, we extensively analyze the behavior of these procedures. Finally, the methods are applied to a data set containing information on the 2016 presidential elections in the USA with unequal and singular empirical covariance matrices. (C) 2017 Elsevier Inc. All rights reserved.

【 授权许可】

Free