Introduction to High-Dimensional Statistics

Giraud, Christophe

  • 出版商: CRC
  • 出版日期: 2021-08-31
  • 售價: $3,350
  • 貴賓價: 9.5$3,183
  • 語言: 英文
  • 頁數: 368
  • 裝訂: Hardcover - also called cloth, retail trade, or trade
  • ISBN: 0367716224
  • ISBN-13: 9780367716226
  • 相關分類: 機率統計學 Probability-and-statistics
  • 立即出貨 (庫存=1)

商品描述

Introduction to High-Dimensional Statistics, Second Edition preserves the philosophy of the first edition: to be a concise guide for students and researchers discovering the area and interested in the mathematics involved. The main concepts and ideas are presented in simple settings, avoiding thereby unessential technicalities. High-dimensional statistics is a fast-evolving field and much progress has been made on a large variety of topics, providing new insights and methods. Offering a succinct presentation of the mathematical foundations of high-dimensional statistics, this new edition features:

 

  • Revised chapters from the previous edition, with the inclusion of many additional materials on some important topics, including compress sensing, estimation with convex constraints, the slope estimator, simultaneously low rank and row sparse linear regression, or aggregation of a continuous set of estimators.

 

 

 

 

 

 

 

 

 

 

 

  • Three new chapters on iterative algorithms, clustering and minimax lower bounds.
  • Enhanced appendices, minimax lower-bounds mainly with the addition of Davis-Kahan perturbation bound and of two simple versions of Hanson-Wright concentration inequality.
  • Covers cutting-edge statistical methods including model selection, sparsity and the lasso, iterative hard thresholding, aggregation, support vector machines and learning theory
  • Provides detailed exercises at the end of every chapter with collaborative solutions on a wikisite.
  • Illustrates concepts with simple but clear practical examples.

 

商品描述(中文翻譯)

《高維統計學導論,第二版》保留了第一版的理念:成為學生和研究人員在探索這一領域並對其中涉及的數學感興趣時的簡明指南。主要概念和思想以簡單的情境呈現,避免不必要的技術細節。高維統計學是一個快速發展的領域,對於各種主題取得了很大進展,提供了新的見解和方法。這本新版提供了高維統計學的數學基礎的簡明介紹,包括以下特點:

- 修訂了上一版的章節,並在一些重要主題上增加了許多額外材料,包括壓縮感知、具有凸約束的估計、斜率估計器、同時低秩和行稀疏線性回歸,或者連續估計器的聚合。

- 新增了三個關於迭代算法、聚類和極小化下界的章節。

- 增強了附錄,主要是增加了Davis-Kahan擾動界限和Hanson-Wright集中不等式的兩個簡單版本的極小化下界。

- 包括最前沿的統計方法,包括模型選擇、稀疏性和套索、迭代硬閾值、聚合、支持向量機和學習理論。

- 每章末尾提供詳細的練習題,並在wikisite上提供協作解答。

- 用簡單而清晰的實際例子來說明概念。

作者簡介

Christophe Giraud was a student of the École Normale Supérieure de Paris, and he received a Ph.D in probability theory from the University Paris 6. He was assistant professor at the University of Nice from 2002 to 2008. He has been associate professor at the École Polytechnique since 2008 and professor at Paris Sud University (Orsay) since 2012. His current research focuses mainly on the statistical theory of high-dimensional data analysis and its applications to life sciences.

作者簡介(中文翻譯)

Christophe Giraud是巴黎高等師範學校的學生,並在巴黎第六大學獲得概率論的博士學位。他在2002年至2008年期間擔任尼斯大學的助理教授。自2008年起,他一直擔任巴黎高等師範學校的副教授,並自2012年起擔任巴黎南大學(奧塞)的教授。他目前的研究主要集中在高維數據分析的統計理論及其在生命科學中的應用。