On testing the equality of high dimensional mean vectors with unequal covariance matrices

In this article, we focus on the problem of testing the equality of several high dimensional mean vectors with unequal covariance matrices. This is one of the most important problem in multivariate statistical analysis and there have been various tests proposed in the literature. Motivated by \citet{BaiS96E} and \cite{ChenQ10T}, a test statistic is introduced and the asymptomatic distributions under the null hypothesis as well as the alternative hypothesis are given. In addition, it is compared with a test statistic recently proposed by \cite{SrivastavaK13Ta}. It is shown that our test statistic performs much better especially in the large dimensional case

MATS: Inference for potentially Singular and Heteroscedastic MANOVA

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, which, however, 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

The inter-temporal stability of real estate returns: an empirical investigation

This paper examines one of the central issues in the formulation of a sector/regional real estate portfolio strategy, i.e. whether the means, standard deviations and correlations between the returns are sufficiently stable over time to justify using ex-post measures as proxies of the ex-ante portfolio inputs required for MPT. To investigate these issues this study conducts a number of tests of the inter-temporal stability of the total returns of the 19 sector/regions in the UK of the IPDMI. The results of the analysis reveal that the theoretical gains in sector and or regional diversification, found in previous work, could not have been readily achieved in practice without almost perfect foresight on the part of an investor as means, standard deviations and correlations, varied markedly from period to period