Weak Convergence and Empirical Processes: With Applications to Statistics
暫譯: 弱收斂與經驗過程：統計應用解析
Van Der Vaart, A. W., Wellner, Jon a.
- 出版商: Springer
- 出版日期: 2023-07-12
- 售價: $6,380
- 貴賓價: 9.5 折 $6,061
- 語言: 英文
- 頁數: 679
- 裝訂: Hardcover - also called cloth, retail trade, or trade
- ISBN: 3031290380
- ISBN-13: 9783031290381
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相關分類:
機率統計學 Probability-and-statistics
海外代購書籍(需單獨結帳)
相關主題
商品描述
This second edition includes many of the new developments in the field since publication of the first edition in 1996: Glivenko-Cantelli preservation theorems; new bounds on expectations ofsuprema of empirical processes; new bounds on covering numbers for various function classes; generic chaining; definitive versions of concentration bounds; and new applications in statistics including penalized M-estimation, the lasso, classification, and support vector machines. The approximately 200 additional pages also round out classical subjects, including chapters on weak convergence in Skorokhod space, on stable convergence, and on processes based on pseudo-observations.
商品描述(中文翻譯)
本書提供了弱收斂理論、經驗過程及其在統計學中各種問題的應用的詳細說明。書的第一部分對隨機收斂的各種形式進行了徹底的探討。第二部分將經驗過程的理論以統計學家和機率學家易於理解的形式整合在一起。在第三部分，作者涵蓋了統計學中的一系列應用，包括估計量的收斂速率；M-估計量和Z-估計量的極限定理；自助法（bootstrap）；函數性δ方法和半參數估計。大多數章節以「問題與補充」作結。其中一些是幫助讀者理解材料的練習，而其他則旨在補充文本。
本書的第二版包含自1996年第一版出版以來該領域的許多新發展：Glivenko-Cantelli保存定理；經驗過程的上確界期望的新界限；各種函數類的覆蓋數的新界限；通用鏈接；集中界限的確定版本；以及在統計學中的新應用，包括懲罰性M-估計、套索（lasso）、分類和支持向量機（support vector machines）。大約200頁的附加內容也補充了經典主題，包括在Skorokhod空間中的弱收斂、穩定收斂以及基於偽觀察的過程的章節。
作者簡介
A.W. van der Vaart is a Professor of Statistics at Delft University, the Netherlands. He earned his Ph.D. in Mathematics from Leiden University. His research interests are in statistics and probability, as mathematical disciplines and in their applications to other sciences, with an emphasis on statistical models with large parameter spaces. He is a member of the Royal Netherlands Academy of Arts and Sciences and recipient of the Spinoza prize. He is a former president of the Netherlands Society for Statistics and Operations Research and served the national and international mathematical and statistical communities in various capacities. He has authored or co-authored eight books, one awarded with the DeGroot prize. Jon A. Wellner is a Professor of Statistics at the University of Washington, Seattle. He earned his Ph.D. in Statistics from the University of Washington. His research interests include uses of large sample theory in statistics, theory of empirical processes and probability in high-dimensional settings, and efficient estimation for semiparametric models. He is also interested in statistical methods under shape constraints. He is a member of the American Association for the Advancement of Science, the Institute of Mathematical Statistics, the Bernoulli Society, and the International Statistical Institute, as well as the Mathematical Association of America, the Society for Industrial and Applied Mathematics, and the American Mathematical Society. He is a past President of the Institute of Mathematical Statistics, has served as an editor or co-editor of the Annals of Statistics and Statistical Science, and has co-authored or co-edited ten books.
作者簡介(中文翻譯)
A.W. van der Vaart 是荷蘭代爾夫特大學的統計學教授。他在萊頓大學獲得數學博士學位。他的研究興趣包括統計學和概率論，作為數學學科及其在其他科學中的應用，特別強調具有大參數空間的統計模型。他是荷蘭皇家藝術與科學學院的成員，也是斯賓諾莎獎的獲得者。他曾擔任荷蘭統計與運籌學會的會長，並在國內外的數學和統計社群中擔任過多種職務。他已經撰寫或共同撰寫了八本書籍，其中一本獲得了德格魯特獎。
Jon A. Wellner 是華盛頓大學西雅圖校區的統計學教授。他在華盛頓大學獲得統計學博士學位。他的研究興趣包括在統計學中使用大樣本理論、實證過程的理論及高維環境中的概率，以及半參數模型的有效估計。他也對形狀約束下的統計方法感興趣。他是美國科學促進會、數學統計學會、伯努利學會和國際統計學會的成員，以及美國數學協會、工業與應用數學學會和美國數學學會的成員。他曾擔任數學統計學會的會長，並擔任《統計年鑑》和《統計科學》的編輯或共同編輯，並共同撰寫或共同編輯了十本書籍。
