Nonparametric Statistics on Stratified Spaces and Their Applications in Object Data Analysis
暫譯: 分層空間上的非參數統計及其在物件數據分析中的應用

Patrangenaru, Victor, Osborne, Daniel E.

Nonparametric Statistics on Stratified Spaces and Their Applications in Object Data Analysis
  • 出版商: CRC
  • 出版日期: 2026-03-15
  • 售價: $5,660
  • 貴賓價: 9.5 折 $5,377
  • 語言: 英文
  • 頁數: 188
  • 裝訂: Hardcover - also called cloth, retail trade, or trade
  • ISBN: 1138043133
  • ISBN-13: 9781138043138
  • 相關分類: 機率統計學 Probability-and-statistics

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商品描述

This book, a follow-up of Nonparametric Statistics on Manifolds and Their Applications to Object Data Analysis where the reader was introduced to data analysis on manifolds, is expanding the subject of data analysis on object spaces, to the case of metric spaces that have a smooth structure on an open dense subset only, governed by a nice filtration structure on the singular part of this space, that is comprised of manifolds whose boundaries are made of lower dimensional manifolds in this filtration. Such object spaces are known as stratified spaces, and their structure will be detailed in the second part of the book. Key examples of complex data from which one extracts data representable as points on a stratified space, and a review on data analysis on manifolds, are provided, alongside a summary of results on nonparametric methods on manifolds. Key results on asymptotic and nonparametric bootstrap on some stratified spaces are included. Certain object spaces with a manifold stratification arising in Statistics are considered with examples of application on data analysis and on them. Various applications include RNA based analysis of the SARSCov2 virus, 3D face identification from digital camera images, English Alphabet based comparison of certain European Languages. Nonparametric Statistics on Stratified Spaces and Their Applications in Object Data Analysis is intended for graduate students to expand their understanding of Nonparametric Statistics, and enhance their ability to grasp and extract complex data and analysis of manifolds.

商品描述(中文翻譯)

這本書是《非參數統計在流形上的應用》（Nonparametric Statistics on Manifolds and Their Applications to Object Data Analysis）的後續作品，讀者在前一本書中已經接觸到流形上的數據分析。本書擴展了對物件空間的數據分析主題，針對僅在開放稠密子集上具有光滑結構的度量空間，這些空間由其奇異部分的良好過濾結構所主導，該結構由邊界為較低維度流形的流形組成。這樣的物件空間被稱為分層空間（stratified spaces），其結構將在本書的第二部分詳細說明。書中提供了從複雜數據中提取可表示為分層空間上點的數據的關鍵範例，以及對流形上數據分析的回顧，並總結了流形上非參數方法的結果。還包括對某些分層空間的漸近和非參數自助法的關鍵結果。考慮到在統計學中出現的具有流形分層的某些物件空間，並提供了在數據分析及其應用上的範例。各種應用包括基於RNA的SARSCov2病毒分析、從數位相機影像中進行的3D人臉識別、以及某些歐洲語言的英文字母比較。《非參數統計在分層空間上的應用》（Nonparametric Statistics on Stratified Spaces and Their Applications in Object Data Analysis）旨在幫助研究生擴展對非參數統計的理解，並增強他們掌握和提取複雜數據及流形分析的能力。

作者簡介

Vic Patrangenaru is a professor in the Statistics Department at Florida State University, Tallahassee, Florida, USA. He is an honored fellow of the Institute of Mathematical Statistics. His research encompasses analysis of complex data types, and the application of projective and differential geometry in various fields, including computer vision, medical imaging and phylogenetics. Throughout his career Dr. Patrangenaru, who guided many doctoral students, spearheaded the new area of Object Data Analysis. He added a new class to the Mathematics Subject Classification 2020, 62R30 Statistics on Manifolds, which is currently in use by Mathematical Reviews and Zentralblatt für Mathematik

Daniel E. Osborne is an associate professor in the Mathematics Department at Florida A&M University, Tallahassee, Florida, USA. As a trained Statistician and Data Science educator, he is dedicated to training student learners and promoting best practices in data literacy, statistical reasoning, data analysis, and data visualization skills among all learners, irrespective of their backgrounds, majors, or career paths.

作者簡介(中文翻譯)

Vic Patrangenaru 是美國佛羅里達州塔拉哈西佛羅里達州立大學統計系的教授。他是數學統計學會的榮譽會員。他的研究涵蓋複雜數據類型的分析，以及投影幾何和微分幾何在各個領域的應用，包括計算機視覺、醫學影像和系統發育學。在他的職業生涯中，Patrangenaru 博士指導了許多博士生，並引領了物件數據分析的新領域。他為數學主題分類 2020 新增了一個類別，62R30 流形上的統計，該類別目前已被《數學評論》和Zentralblatt für Mathematik 使用。

Daniel E. Osborne 是美國佛羅里達州塔拉哈西佛羅里達A&M大學數學系的副教授。作為一名受過訓練的統計學家和數據科學教育者，他致力於培訓學生學習者，並在所有學習者中推廣數據素養、統計推理、數據分析和數據可視化技能的最佳實踐，無論他們的背景、專業或職業道路如何。

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