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 extreme value statistics, the tail index is an important measure to gauge the heavy-tailed behavior of a distribution. Under Pareto-type distributions, we employ the logarithmic function to link the tail index to the linear predictor induced by covariates, which constitutes the tail index...

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 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...

We consider here a large-scale social network with a continuous response observed for each node at equally spaced time points. The responses from different nodes constitute an ultra-high dimensional vector, whose time series dynamic is to be investigated. In addition, the network structure is...

In social network analysis, many estimation methods have been developed over the past three decades. Due to the computational complexity for analyzing large-scale social network data, however, those methods cannot be applied effectively. On the other hand, the structure of large-scale network...

Subgroup analysis is an integral part of comparative analysis where assessing the treatment effect on a response is of central interest. Its goal is to determine the heterogeneity of the treatment effect across subpopulations. In this paper, we adapt the idea of recursive partitioning and...

In high dimensional data analysis, we propose a sequential model averaging (SMA) method to make accurate and stable predictions. Specifically, we in- troduce a hybrid approach that combines a sequential screening process with a model averaging algorithm, where the weight of each model is...

The mean-variance theory of Markowitz (1952) indicates that large investment portfolios naturally provide better risk diversi cation than small ones. However, due to parameter estimation errors, one may find ambiguous results in practice. Hence, it is essential to identify relevant stocks to...

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...