Skip to search formSkip to main contentSkip to account menu

On asymptotically optimal confidence regions and tests for high-dimensional models

A general method for constructing confidence intervals and statistical tests for single or low-dimensional components of a large parameter vector in a high-dimensional model and develops the corresponding theory which includes a careful analysis for Gaussian, sub-Gaussian and bounded correlated designs.
View PDF on arXiv (opens in a new tab)

Empirical Processes in M-Estimation

A global test for groups of genes: testing association with a clinical outcome

A global test to be used for the analysis of microarray data to determine whether the global expression pattern of a group of genes is significantly related to some clinical outcome of interest.
View on PubMed (opens in a new tab)

HIGH-DIMENSIONAL GENERALIZED LINEAR MODELS AND THE LASSO

  • S. Geer
  • Computer Science, Mathematics
  • 1 April 2008
A nonasymptotic oracle inequality is proved for the empirical risk minimizer with Lasso penalty for high-dimensional generalized linear models with Lipschitz loss functions, and the penalty is based on the coefficients in the linear predictor, after normalization with the empirical norm.
View PDF on arXiv (opens in a new tab)

On the conditions used to prove oracle results for the Lasso

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 this paper how the…
View PDF on arXiv (opens in a new tab)

Statistics for High-Dimensional Data: Methods, Theory and Applications

This book presents a detailed account of recently developed approaches, including the Lasso and versions of it for various models, boosting methods, undirected graphical modeling, and procedures controlling false positive selections.

Oracle Inequalities and Optimal Inference under Group Sparsity

The Group Lasso can achieve an improvement in the prediction and estimation properties as compared to the Lasso, and it is proved that the rate of convergence of the upper bounds is optimal in a minimax sense.
View PDF on arXiv (opens in a new tab)

Applications of empirical process theory

Preface Reading guide 1. Introduction 2. Notations and definitions 3. Uniform laws of large numbers 4. First applications: consistency 5. Increments of empirical processes 6. Central limit theorems…

Statistics for High-Dimensional Data

View via Publisher (opens in a new tab)

ℓ1-penalization for mixture regression models

We consider a finite mixture of regressions (FMR) model for high-dimensional inhomogeneous data where the number of covariates may be much larger than sample size. We propose an ℓ1-penalized maximum…
View on Springer (opens in a new tab)
...
By clicking accept or continuing to use the site, you agree to the terms outlined in our Privacy Policy (opens in a new tab), Terms of Service (opens in a new tab), and Dataset License (opens in a new tab)