Estimation and Testing Under Sparsity

École d'Été de Probabilités de Saint-Flour XLV – 2015

  • Sara van de Geer

Part of the Lecture Notes in Mathematics book series (LNM, volume 2159)

Also part of the École d'Été de Probabilités de Saint-Flour book sub series (LNMECOLE, volume 2159)

Table of contents

  1. Front Matter
    Pages i-xiii
  2. Sara van de Geer
    Pages 1-4
  3. Sara van de Geer
    Pages 5-25
  4. Sara van de Geer
    Pages 27-39
  5. Sara van de Geer
    Pages 61-74
  6. Sara van de Geer
    Pages 75-101
  7. Sara van de Geer
    Pages 103-119
  8. Sara van de Geer
    Pages 121-131
  9. Sara van de Geer
    Pages 133-137
  10. Sara van de Geer
    Pages 151-165
  11. Sara van de Geer
    Pages 167-197
  12. Sara van de Geer
    Pages 199-214
  13. Sara van de Geer
    Pages 223-231
  14. Sara van de Geer
    Pages 233-238
  15. Sara van de Geer
    Pages 239-253
  16. Sara van de Geer
    Pages 255-266
  17. Back Matter
    Pages 267-276

About this book

Introduction

Taking the Lasso method as its starting point, this book describes the main ingredients needed to study general loss functions and sparsity-inducing regularizers. It also provides a semi-parametric approach to establishing confidence intervals and tests. Sparsity-inducing methods have proven to be very useful in the analysis of high-dimensional data. Examples include the Lasso and group Lasso methods, and the least squares method with other norm-penalties, such as the nuclear norm. The illustrations provided include generalized linear models, density estimation, matrix completion and sparse principal components. Each chapter ends with a problem section. The book can be used as a textbook for a graduate or PhD course.

Keywords

62-XX; 60-XX, 68Q87 high-dimensional statistics sparsity empirical risk minimization oracle inequality

Authors and affiliations

  • Sara van de Geer
    • 1
  1. 1.Seminar für Statistik HGG 24.1ETH ZentrumZürichSwitzerland

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-319-32774-7
  • Copyright Information Springer International Publishing Switzerland 2016
  • Publisher Name Springer, Cham
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-3-319-32773-0
  • Online ISBN 978-3-319-32774-7
  • Series Print ISSN 0075-8434
  • Series Online ISSN 1617-9692
  • About this book