Estimation and Testing Under Sparsity

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École d’Été de Probabilités de Saint-Flour XLV – 2015, Lecture Notes in Mathematics 2159 – École d’Été de Probabilités de Saint-Flour

ISBN: 3319327739
ISBN 13: 9783319327730
Autor: van de Geer, Sara
Verlag: Springer Verlag GmbH
Umfang: xiii, 274 S.
Erscheinungsdatum: 29.06.2016
Auflage: 1/2016
Produktform: Kartoniert
Einband: Kartoniert

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.

Beschreibung

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.

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E-Mail: juergen.hartmann@springer.com

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