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École d'Été de Probabilités de Saint-Flour

Estimation and Testing Under Sparsity

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

Authors: van de Geer, Sara

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  • Starting with the popular Lasso method as its prime example, the book then extends to a broad family of estimation methods for high-dimensional data
  • A theoretical basis for sparsity-inducing methods is provided, together with ways to build confidence intervals and tests
  • The focus is on common features of methods for high-dimensional data and, as such, a potential starting point is given for the analysis of other methods not treated in the book
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eBook $44.99
price for USA in USD (gross)
  • ISBN 978-3-319-32774-7
  • Digitally watermarked, DRM-free
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  • Immediate eBook download after purchase
Softcover $59.99
price for USA in USD
  • ISBN 978-3-319-32773-0
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
About this book

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.

Reviews

“This book is presented as a series of lecture notes on the theory of penalized estimators under sparsity. … The level of detail is high, and almost all proofs are given in full, with discussion. Each chapter ends with a section of problems, which could be used in a study setting to improve understanding of the proofs.” (Andrew Duncan A. C. Smith, Mathematical Reviews, August, 2017)

“The book provides several examples and illustrations of the methods presented and discussed, while each of its 17 chapters ends with a problem section. Thus, it can be used as textbook for students mainly at postgraduate level.” (Christina Diakaki, zbMATH 1362.62006, 2017)


Table of contents (18 chapters)

Table of contents (18 chapters)

Buy this book

eBook $44.99
price for USA in USD (gross)
  • ISBN 978-3-319-32774-7
  • Digitally watermarked, DRM-free
  • Included format: PDF, EPUB
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Softcover $59.99
price for USA in USD
  • ISBN 978-3-319-32773-0
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
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Bibliographic Information

Bibliographic Information
Book Title
Estimation and Testing Under Sparsity
Book Subtitle
École d'Été de Probabilités de Saint-Flour XLV – 2015
Authors
Series Title
École d'Été de Probabilités de Saint-Flour
Series Volume
2159
Copyright
2016
Publisher
Springer International Publishing
Copyright Holder
Springer International Publishing Switzerland
eBook ISBN
978-3-319-32774-7
DOI
10.1007/978-3-319-32774-7
Softcover ISBN
978-3-319-32773-0
Series ISSN
0721-5363
Edition Number
1
Number of Pages
XIII, 274
Topics