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

"Tests for Multivariate Analysis of Variance in High Dimension Under Non-Normality"

In this article, we consider the problem of testing the equality of mean vectors of dimension ρ of several groups with a common unknown non-singular covariance matrix Σ, based on N independent observation vectors where N may be less than the dimension ρ. This problem, known in the literature as the Multivariate Analysis of variance (MANOVA) in high-dimension has recently been considered in the statistical literature by Srivastava and Fujikoshi[7], Srivastava [5] and Schott[3]. All these tests are not invariant under the change of units of measurements. On the lines of Srivastava and Du[8] and Srivastava[6], we propose a test that has the above invariance property. The null and the non-null distributions are derived under the assumption that ( N, ρ) → ∞ and N may be less than ρ and the observation vectors follow a general non-normal model.

Testing the Sphericity of a covariance matrix when the dimension is much larger than the sample size

This paper focuses on the prominent sphericity test when the dimension $p$ is much lager than sample size $n$. The classical likelihood ratio test(LRT) is no longer applicable when $p\gg n$. Therefore a Quasi-LRT is proposed and asymptotic distribution of the test statistic under the null when $p/n\rightarrow\infty, n\rightarrow\infty$ is well established in this paper. Meanwhile, John's test has been found to possess the powerful {\it dimension-proof} property, which keeps exactly the same limiting distribution under the null with any $(n,p)$-asymptotic, i.e. $p/n\rightarrow[0,\infty]$, $n\rightarrow\infty$. All asymptotic results are derived for general population with finite fourth order moment. Numerical experiments are implemented for comparison

Non-Linear Markov Modelling Using Canonical Variate Analysis: Forecasting Exchange Rate Volatility

We report on a novel forecasting method based on nonlinear Markov modelling and canonical variate analysis, and investigate the use of a prediction algorithm to forecast conditional volatility. In particular, we assess the dynamic behaviour of the model by forecasting exchange rate volatility. It is found that the nonlinear Markov model can forecast exchange rate volatility significantly better than the GARCH(1,1) model due to its flexibility in accommodating nonlinear dynamic patterns in volatility, which are not captured by the linear GARCH(1,1) model.