LEADER 02842nam a2200385 i 4500 001 991003507699707536 006 m d 007 cr n 008 180601s2016 nyu 000 0 eng d 020 $a9783319327730 (alk. paper) 035 $ab14343903-39ule_inst 040 $aBibl. Dip.le Aggr. Matematica e Fisica - Sez. Matematica$beng 082 04$a519.2$223 084 $aAMS 62J07 100 1 $aGeer, Sara A. van de$0534659 245 10$aEstimation and testing under sparsity$h[e-book] :$bÉcole d'Été de Probabilités de Saint-Flour XLV ? 2015 /$cby Sara van de Geer 263 $a1606 264 1$aCham :$bSpringer,$c2016 300 $a1 online resource (xiii, 274 p.) 336 $atext$btxt$2rdacontent 337 $aunmediated$bn$2rdamedia 338 $avolume$bnc$2rdacarrier 490 1 $aLecture Notes in Mathematics,$x0075-8434 ;$v2159 505 0 $a1 Introduction ; The Lasso ; 3 The square-root Lasso ; 4 The bias of the Lasso and worst possible sub-directions ; 5 Confidence intervals using the Lasso ; 6 Structured sparsity ; 7 General loss with norm-penalty ; 8 Empirical process theory for dual norms ; 9 Probability inequalities for matrices ; 10 Inequalities for the centred empirical risk and its derivative ; 11 The margin condition ; 12 Some worked-out examples ; 13 Brouwer?s fixed point theorem and sparsity ; 14 Asymptotically linear estimators of the precision matrix ; 15 Lower bounds for sparse quadratic forms ; 16 Symmetrization, contraction and concentration ; 17 Chaining including concentration ; 18 Metric structure of convex hulls 520 $aTaking the Lasso method as its starting point, this book describes the main ingredients needed to study general loss functions and sparsity-inducing regularizers. It also provides a semi-parametric approach to establishing confidence intervals and tests. Sparsity-inducing methods have proven to be very useful in the analysis of high-dimensional data. Examples include the Lasso and group Lasso methods, and the least squares method with other norm-penalties, such as the nuclear norm. The illustrations provided include generalized linear models, density estimation, matrix completion and sparse principal components. Each chapter ends with a problem section. The book can be used as a textbook for a graduate or PhD course 650 0$aMathematical statistics 650 0$aProbabilities 773 0 $aSpringer eBooks 776 08$iPrinted edition:$z9783319327730 856 40$uhttps://link.springer.com/book/10.1007/978-3-319-32774-7$zAn electronic book accessible through the World Wide Web 907 $a.b14343903$b03-03-22$c01-06-18 912 $a991003507699707536 996 $aEstimation and testing under sparsity$91748813 997 $aUNISALENTO 998 $ale013$b01-06-18$cm$d@ $e-$feng$gsz $h0$i0