Gaussian multiplier bootstrap in high dimension with applications to model selection

Since its introduction in 1979 by Efron, the bootstrap became one of the most popular and effective methods in various statistical problems like confidence estimation, hypothesis testing, model selection, etc. However, validation of a bootstrap procedure is very involved and requires some advance tools from empirical process theory and Gaussian processes.
Most of these tools meet serious problems and challenges if the parameter dimension becomes large, much larger than the sample size. Recently Chernozhkov et al (2013, 2014) offered a new approach to statistical inference in high dimension which includes powerful result for Gaussian processes and random matrices, Gaussian approximation in high dimension, and Gaussian comparison. This talk reviews some of these results and tools and explains how they can be applied to the problems of subset estimation and sparse estimation problems.