Efromovich Sam. Nonparametric Curve Estimation: methods, theory and applications

Springer, 1999. — 423 p.Appropriate for a one-semester course, this self-contained book is an introduction to nonparametric curve estimation theory. It may be used for teaching graduate students in statistics (in this case an intermediate course in statistical inference, on the level of the book by Casella and Berger (1990), is the prerequisite) as well as for diverse classes with students from other sciences including engineering, business, social, medical, and biological among others (in this case a traditional intermediate calculus course plus an introductory course in probability, on the level of the book by Ross (1997), are the prerequisites).There are several distinguishing features of this book that should be highlighted:
- All basic statistical models, including probability density estimation, nonparametric regression, time series analysis including spectral analysis, and filtering of time-continuous signals, are considered as one general problem. As a result, universal methods of estimation are discussed, and students become familiar with a wide spectrum of applications of nonparametric methods.
- Main emphasis is placed on the case of small sample sizes and datadriven orthogonal series estimates (Chapters 1–6). Chapter 7 discusses (with proofs) modern asymptotic results, and Chapter 8 is devoted to a thorough discussion of nonseries methods.
- The companion software package (available over the World Wide Web) allows students to produce and modify almost all figures of the book as well as to analyze a broad spectrum of simulated and real data sets. Based on the S–PLUS environment, this package requires no knowledge of S–PLUS and is elementary to use. Appendix B explains how to install and use this package; it also contains information about the affordable S–PLUS Student Edition for PC.
- “Practical Seminar” sections are devoted to applying the methods studied to the analysis and presentation of real data sets. The software for these sections allows students to analyze any data set that exists in the S–PLUS environment.
- “Case Study” sections allow students to explore applications of basic methods to more complicated practical problems. These sections together with “Special Topic” sections give the instructor some flexibility in choosing additional material beyond the core.
- Plenty of exercises with different levels of difficulty will allow the instructor to keep students with different mathematical and statistical backgrounds out of trouble! - “Notes” sections at the end of each chapter are primarily devoted to books for further reading. They also capture some bibliographic comments, side issues, etc.
- Appendix A contains a brief review of fundamentals of statistical inference. All the related notions and notations used in the book may be found there. It is highly recommended to review these fundamentals prior to studying Chapters 3–8. Also, exercises for Appendix A may be used as a first quiz or homework. A bit of advice to the reader who would like to use this book for self-study and who is venturing for the first time into this area. You can definitely just read this book as any other text without using the companion software. There are plenty of figures (more than a hundred), which will guide you through the text. However, if you have decided to study nonparametrics, then you are probably interested in data analysis. I cannot stress too strongly the importance of combining reading with analyzing both simulated and real data sets. This is the kind of experience that you can gain only via repeated exercises, and here the software can make this process dramatically quicker and less painful. Using the software will allow you to check virtually every claim and development mentioned in the book and make the material fully transparent. Also, please review the fundamentals outlined in Appendix A prior to studying Chapters 3–8.