Learning from Data: Concepts, Theory, and Methods
Learning from Data: Concepts, Theory, and Methods
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DOI：
10.1198/tech.2001.s558
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发表时间：
2001-02
期刊：
影响因子：
2.5
通讯作者：
R. Lordo
中科院分区：
文献类型：
--
作者：
R. Lordo
这本书包括一个新的小波技术，可用于探索几种类型的统计问题，包括但不限于非参数回归，密度估计和变点问题的集合。它提供了一个简单但坚实的介绍，从应用的角度来看，可用的小波工具。这本书的主要焦点似乎是发展的应用方面的统计功能估计使用各种小波方法。这本书的目的是作为高级本科生到研究生课程的参考。它完全依赖于几个工作的例子，并提供了一步一步的方法，为大多数说明的例子。对于那些想要用小波工具弄脏自己的手的读者来说，这绝对是一个加分。事实上，读者可能想从作者引用的网站上下载S-PLUS代码。介绍性章节提供了小波基本理论的概述，这些结果在整个文本中使用。在这本书所涵盖的基本议题是二进小波，时间频率局部化，小波变换，框架，样条小波，正交小波基，小波包。此外，作者提出了推广和扩展的二维小波和平移不变小波平滑。这本书需要本科微积分，线性代数和基本统计理论的背景。本书的“肉”部分在于其第4章，作者在其中提出了几个“小波特征和例子”小波分解和重构的基本理论是以一种易于遵循的方式提出的，并且不需要大量的泛函分析高级理论知识。然后，作者介绍了滤波器表示和时频局部化的基本概念。最后，所有上述主题，然后说明通过几个小波的例子。第6章和第7章为任何对基于小波的模型的统计推断感兴趣但不一定是专家的研究人员提供了基本概念。这本书已经实现了它的目标，提出了基本小波概念，在一个可以理解的方式，以观众熟悉的基本理论统计。这本书的中心主题似乎集中在使用现成的小波工具分析几个统计模型。每一章所涵盖的材料有时似乎是有限的，强调几何上诉小波没有得到解决。总之，统计应用和数据分析的基本小波工具很好地介绍了小波工具来解释统计建模的各个方面。这本书的一个非常好的方面是，它提供了一个网站参考，其中包含了大多数额外的资源，如用于生成书中使用的图形的S-PLUS代码。然而，这本书缺乏优雅的几何方法的小波方法，但这是部分性质的材料。这些基本的几何概念对初学者来说可能是难以理解的。不幸的是，大多数关于小波的书籍主要是研究统计学家可以访问的。这本书介绍了基本和先进的概念小波的方式是访问任何人只有一个基本的知识统计和数学理论。读者可能还想读一本维达科维奇（Vidakovic，1999）的书，这本书也提出了与本书类似的观点。我非常喜欢这本书，并会毫不犹豫地推荐它的使用在课堂上作为参考书的课程统计推断的基础上小波模型。
This book consists of a collection of new wavelet techniques that can be used to explore several types of statistical problems, including but not limited to nonparametric regression, density estimation, and change-point problems. It provides an easy but solid introduction to available wavelet tools from an applied point of view. The main focus of this book seems to be development of the applied aspects of statistical functional estimation using a variety of wavelet methods. This book is intended as a reference for advanced undergraduateto graduate-level courses. It relies exclusively on several worked-out examples and provides step-by-step methods for most of the illustrated examples. This is de nitely a plus point for readers who want to get their hands dirty with wavelet tools. In fact, the reader may want to download the S-PLUS codes from the Web site cited by the author. The introductory chapters provide an overview of essential theory of wavelets, and these results are used throughout the text. Among the basic topics covered in this book are dyadic wavelets, time-frequency localization, wavelet transforms, frames, spline wavelets, orthonormal wavelet bases, and wavelet packets. In addition, the author presents generalizations and extensions to twodimensional wavelets and translation-invariant wavelet smoothing. The book requires a background in undergraduate calculus, linear algebra, and basic statistical theory. The “meat” part of the book lies in its Chapter 4, in which the author presents several “wavelet features and examples.” The essential theory on wavelet decomposition and reconstruction is presented in a manner that is easy to follow and does not require substantial knowledge of advanced theory of functional analysis. The author then presents fundamental concepts of lter representation and time-frequency localization. Finally, all of the aforementioned topics are then illustrated via several wavelet examples. Chapters 6 and 7 provide essential concepts for any researcher who is interested in statistical inference for wavelet-based models but is not necessarily an expert in either. The book has achieved its goal of presenting basic wavelet concepts in an understandable way to an audience familiar with the basic theory of statistics. The central theme of the book seems to focus on analyzing several statistical models using ready-made wavelet tools. The material covered in each chapter sometimes seems limited; emphasis on geometrical appeal to wavelets is not addressed. In summary, Essential Wavelets for Statistical Applications and Data Analysis does a good job of presenting wavelet tools to explain various aspects of statistical modeling. A very nice aspect of this book is that it provides a Web site reference that contains most additional resources, such as S-PLUS codes that were used to generate graphics used in the book. However, the book lacks the elegant geometrical approach of wavelet methods, but that is partially the nature of the material. Such fundamental geometrical concepts might turn out to be dif cult to follow for the beginners. Unfortunately, most books on wavelets are primarily accessible to research statisticians. This book presents basic and advanced concepts of wavelets in a way that is accessible to anyone with only a fundamental knowledge of statistical and mathematical theory. The reader may also want to read a book by Vidakovic (1999) that also presents ideas similar to those developed in this one. I liked the book very much and would not hesitate to recommend its usage in a classroom as reference book for a course on statistical inference based on wavelet models.