Differential entropy and log determinant of the covariance matrix of a multivariate Gaussian distribution have many applications in coding, communications, signal processing and statistical inference. In this paper we consider in the high-dimensional setting optimal estimation of the...

Motivated by analysis of genetical genomics data, we introduce a sparse high-dimensional multivariate regression model for studying conditional independence relationships among a set of genes adjusting for possible genetic effects. The precision matrix in the model specifies a covariate-adjusted...

This article proposes a new formulation for the construction of adaptive confidence bands (CBs) in nonparametric function estimation problems. CBs, which have size that adapts to the smoothness of the function while guaranteeing that both the relative excess mass of the function lying outside...

This paper considers testing the equality of multiple high-dimensional mean vectors under dependency. We propose a test that is based on a linear transformation of the data by the precision matrix which incorporates the dependence structure of the variables. The limiting null distribution of the...

type="main" xml:id="rssb12034-abs-0001" <title type="main">Summary</title> <p>The paper considers in the high dimensional setting a canonical testing problem in multivariate analysis, namely testing the equality of two mean vectors. We introduce a new test statistic that is based on a linear transformation of the data by the...</p>

type="main" xml:id="rssb12064-abs-0001" <title type="main">Summary</title> <p>The paper develops a unified theoretical and computational framework for false discovery control in multiple testing of spatial signals. We consider both pointwise and clusterwise spatial analyses, and derive oracle procedures which optimally...</p>