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Assigning statistical significance in high-dimensional problems

Peter Bühlmann

Recorded 08 July 2013 in Lausanne, Vaud, Switzerland

Event: Spars 2013 - Signal Processing with Adaptive Sparse Structured Representations

Abstract

High-dimensional data, where the number of variables is much larger than sample size, occur in many applications nowadays. During the last decade, remarkable progress has been achieved in terms of point estimation and computation. However, one of the core statistical tasks, namely to quantify uncertainty or to assign statistical signi?cance, is still in its infancy for many problems and models. After a brief review of some main concepts for high-dimensional statistical inference, we present procedures and corresponding (optimality) theory for quantifying signi?cance in high-dimensional settings, including linear and generalized linear models. Illustration on various examples highlights the methods’ user-friendly nature for high-dimensional data analysis.

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