In a high dimensional linear regression model, we propose a new procedure for testing statistical significance of a subset of regression coefficients. Specifically, we employ the partial covariances between the response variable and the tested covariates to obtain a test statistic. The resulting...

This article introduces covariance regression analysis for a p-dimensional response vector. The proposed method explores the regression relationship between the p-dimensional covariance matrix and auxiliary information. We study three types of estimators: maximum likelihood, ordinary least...

In multivariate analysis, the covariance matrix associated with a set of variables of interest (namely response variables) commonly contains valuable information about the dataset. When the dimension of response variables is considerably larger than the sample size, it is a non-trivial task to...

In this article, we employ a regression formulation to estimate the high dimensional covariance matrix for a given network structure. Using prior information contained in the network relationships, we model the covariance as a polynomial function of the symmetric adjacency matrix. Accordingly,...

In this paper, we propose two important measures, quantile correlation (QCOR) and quantile partial correlation (QPCOR). We then apply them to quantile autoregressive (QAR) models, and introduce two valuable quantities, the quantile autocorrelation function (QACF) and the quantile partial...