Name: Johnstone

Firstname: Iain

Title: Prof

Institution: Dept of Statistics, Sequoia Hall

Street: 390 Serra Mall

City: Stanford University, CA

Zip-Code: 94305

Country: USA

Phone: 1 650 723 9114

Fax: 1 650 725 8977


Authors: F. Abramovich, Y. Benjamini, D. Donoho, I. Johnstone

Title: False discovery rates and the estimation of sparse normal means

Abstract: We attempt to recover a high-dimensional vector observed in white noise, where the vector is known to be sparse, but the degree of sparsity is unknown. Here sparsity may be thought of as the fraction of nonzero terms. We obtain a procedure which is asymptotically minimax for a variety of error measures, simultaneously throughout a range of sparsity classes.

The optimal procedure is a data-adaptive thresholding scheme, driven by control of the False Discovery Rate (FDR). Previous results will be reviewed, as well as recent work that says that letting $q_n \rightarrow q \in [0,1/2]$ with problem size $n$ is sufficient for asymptotic minimaxity, while keeping fixed $q > 1/2$ prevents asymptotic minimaxity.

Our work provides a new perspective on a class of model selection rules which has been introduced recently by several authors. These new rules impose complexity penalization of the form $2 \cdot \log( \mbox{ potential model size } / \mbox{ actual model size } )$. We exhibit a close connection with FDR-controlling procedures.