The breakthrough of microarray technology is a vital research instrument to measure the quantitative and highly parallel of gene expression. In microarray studies, it is common that the data set typically consists of tens of thousands of genes (variables) from just dozens of samples due to various constraints including the high cost of producing microarray chips. As a result, the combined sampl...

We consider the estimation of integrated covariance matrices of high dimensional diffusion processes by using high frequency data. We start by studying the most commonly used estimator, the realized covariance matrix (RCV). We show that in the high dimensional case when the dimension p and the observation frequency n grow in the same rate, the limiting empirical spectral distribution of RCV dep...

We propose an appearance manifold with view-dependent covariance matrix for face recognition from video sequences in two learning frameworks: the supervised-learning and the incremental unsupervisedlearning. The advantages of this method are, first, the appearance manifold with view-dependent covariance matrix model is robust to pose changes and is also noise invariant, since the embedded covar...

In this paper, we study the problem of estimating covariance matrix under differential privacy, where underlying is assumed to be sparse and high dimensions. We propose a new method, called DP-Thresholding, achieve non-trivial ℓ2-norm based error bound whose dependence on dimension drops logarithmic instead polynomial, it significantly better than existing ones, which add noise directly empiric...

We propose a test for covariance matrix to have Kronecker Product Structure (KPS). KPS implies reduced rank restriction on certain transformation of the and new procedure is an adaptation Kleibergen Paap (2006) test. To derive limiting distribution Wald type statistic proves challenging partly because singularity estimator that appears in weighting matrix. show has ? 2 null with degrees freedom...