Estimation and Testing Under Sparsity École d'Été de Probabilités de Saint-Flour XLV – 2015 /

• Main Author: van de Geer, Sara (Author)
• Corporate Author: SpringerLink (Online service)
• Format: Electronic eBook
• Language: English
• Published: Cham : Springer International Publishing : Imprint: Springer, 2016.
• Series: Lecture Notes in Mathematics, 2159
• Subjects: Mathematics.; Mathematical statistics.; Probabilities.; Statistics.; Probability Theory and Stochastic Processes.; Statistical Theory and Methods.; Probability and Statistics in Computer Science.
• Physical Description: XIII, 274 p. online resource.
• ISBN: 9783319327747
• ISSN: 0075-8434 ;

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.