Introduction to Functional Data Analysis

Introduction to Functional Data Analysis provides a concise textbook introduction to the field. It explains how to analyze functional data, both at exploratory and inferential levels. It also provides a systematic and accessible exposition of the methodology and the required mathematical framework.

The book can be used as textbook for a semester-long course on FDA for advanced undergraduate or MS statistics majors, as well as for MS and PhD students in other disciplines, including applied mathematics, environmental science, public health, medical research, geophysical sciences and economics. It can also be used for self-study and as a reference for researchers in those fields who wish to acquire solid understanding of FDA methodology and practical guidance for its implementation. Each chapter contains plentiful examples of relevant R code and theoretical and data analytic problems.

The material of the book can be roughly divided into four parts of approximately equal length: 1) basic concepts and techniques of FDA, 2) functional regression models, 3) sparse and dependent functional data, and 4) introduction to the Hilbert space framework of FDA. The book assumes advanced undergraduate background in calculus, linear algebra, distributional probability theory, foundations of statistical inference, and some familiarity with R programming. Other required statistics background is provided in scalar settings before the related functional concepts are developed. Most chapters end with references to more advanced research for those who wish to gain a more in-depth understanding of a specific topic.

《功能數據分析入門》是一本簡明的教科書，介紹了這個領域的基礎知識。它解釋了如何在探索性和推論性層面上分析功能數據。同時，它還提供了方法論和所需數學框架的系統和易於理解的闡述。

這本書可以作為高年級本科生或碩士統計專業FDA課程的教材，也可以用於其他學科的碩士和博士生，包括應用數學、環境科學、公共衛生、醫學研究、地球物理科學和經濟學。它還可以用於自學，以及作為那些希望獲得FDA方法論的扎實理解和實踐指南的研究人員的參考。每章都包含了豐富的相關R代碼示例和理論和數據分析問題。

這本書的內容可以大致分為四個部分，每個部分的長度大致相等：1）FDA的基本概念和技術，2）功能回歸模型，3）稀疏和相關的功能數據，以及4）介紹FDA的希爾伯特空間框架。本書假設讀者具有微積分、線性代數、分佈概率論、統計推斷基礎以及對R編程的一定熟悉程度的高年級本科背景。在相關的功能概念被發展之前，書中提供了所需的統計背景知識。大多數章節結束時都會提供更深入研究的參考文獻，以供那些希望對特定主題有更深入了解的人參考。