Associate to each subset of the integers its almost sure limiting relative frequency under the Bernouilli random walk, if it has one. The resulting probability space is purely finitely additive, and uniform in the sense of residue classes and shift-invariance. However, it is not uniform in the...

Since James and Stein's seminal work, the problem of "estimating n normal means" has received plenty of enthusiasm in the statistics community. Recently, driven by the fast expansion of the field of large-scale multiple testing, there has been a resurgence of research interest in the "n" normal...

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...

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...