Recursive partitioning methods have become popular and widely used tools for
nonparametric regression and classification in many scientific fields. Especially random …

During the past decade there has been an explosion in computation and information
technology. With it have come vast amounts of data in a variety of fields such as medicine …

The idea for this book came from the time the authors spent at the Statistics and Applied
Mathematical Sciences Institute (SAMSI) in Research Triangle Park in North Carolina …

We show that, under a sparsity scenario, the Lasso estimator and the Dantzig selector
exhibit similar behavior. For both methods, we derive, in parallel, oracle inequalities for the …

Finding sparse approximate solutions to large underdetermined linear systems of equations
is a common problem in signal/image processing and statistics. Basis pursuit, the least …

We consider the problem of model selection and estimation in situations where the number
of parameters diverges with the sample size. When the dimension is high, an ideal method …

The problem of consistently estimating the sparsity pattern of a vector beta* isin R p based
on observations contaminated by noise arises in various contexts, including signal …

Oracle inequalities and variable selection properties for the Lasso in linear models have
been established under a variety of different assumptions on the design matrix. We show in …

The Lasso is an attractive technique for regularization and variable selection for high-
dimensional data, where the number of predictor variables pn is potentially much larger than …

Variable selection in high-dimensional space characterizes many contemporary problems in
scientific discovery and decision making. Many frequently-used techniques are based on …