Estimation and Testing Under Sparsity

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

• Author(s): Sara van de Geer,
• Publisher: Springer
• Pages: 274
• ISBN_10: 3319327747
  ISBN_13: 9783319327747
  
• Language: en
• Categories: Mathematics / Probability & Statistics / General , Computers / Mathematical & Statistical Software , Mathematics / Probability & Statistics / Stochastic Processes , Mathematics / Discrete Mathematics ,

Description:... 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.