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AbstractA simple test is proposed to test the independence of high-dimensional random normal vectors. The method consists of two steps. First, the primary high-dimensional data is projected onto a low-dimensional subspace multiple times using random projection matrices. Second, the test statistic is constructed by utilizing the classical statistics obtained from the projected low-dimensional datasets. Simulations are performed to compare the performance of the proposed test with existing state-of-the-art tests, in terms of test sizes and powers. Finally, the proposed methodology is illustrated using two gene datasets, namely the Colon and Leukemia cancer datasets. [ABSTRACT FROM AUTHOR]

Seemingly unrelated regression (SUR) models were applied when several linear regression equations were investigated at the same time. To reduce the multicollinearity influence in the SUR models, the one-parameter ridge (Ridge-1) solution was proposed and discussed by some researchers. As a generalization of the Ridge-1 solution, in the context of SUR models having multicollinearity problem, the two-parameter ridge (Ridge-2) solution was presented. Some simulations were performed to compare the proposed solution with the ordinary generalized least squares (GLS) and Ridge-1 solutions. Lastly, the proposed solution was applied on chronic renal failure effect data. [ABSTRACT FROM AUTHOR]

So called multiple correlation coefficient (MCC) is a measure of linear relationship between a given variable and set of covariates. In the multiple correlation and regression analysis, it is common practice to construct a confidence interval for the population MCC. In high-dimensional data settings, by which the data dimension p is much larger than the sample size n, due to the singularity of the sample covariance matrix, the classical confidence intervals for the MCC are no longer useable. For high-dimensional elliptical data, some (conservative) confidence intervals for the population MCC are presented using the random projection methodology. To evaluate and compare the performance of the proposed confidence intervals, some simulations are conducted in terms of the coverage probability and average interval length. Experimental validation of the proposed intervals is carried out on two real gene expression datasets. [ABSTRACT FROM AUTHOR]

In this paper, some confidence intervals (CIs) for the product of powers of the generalized variances of k multivariate normal populations with possibly different dimensions are proposed. The performance of these CIs in terms of the coverage probabilities and average lengths were evaluated via a Monte Carlo simulation study. The results were found to be satisfactory. To demonstrate utility of the proposed CIs, applications on three real data sets were provided. [ABSTRACT FROM AUTHOR]

Generalized variance is a measure of dispersion of multivariate data. Comparison of dispersion of multivariate data is one of the favorite issues for multivariate quality control, generalized homogeneity of multidimensional scatter, etc. In this article, the problem of testing equality of generalized variances of k multivariate normal populations by using the Bartlett's modified likelihood ratio test (BMLRT) is proposed. Simulations to compare the Type I error rate and power of the BMLRT and the likelihood ratio test (LRT) methods are performed. These simulations show that the BMLRT method has a better chi-square approximation under the null hypothesis. Finally, a practical example is given. [ABSTRACT FROM AUTHOR]