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Nonparametric curve estimation. Methods, theory, and applications. (English) Zbl 0935.62039

Springer Series in Statistics. New York, NY: Springer. xiii, 411 p. (1999).
This book is a comprehensive and very readable introduction to nonparametric curve estimation theory. It gives a unified approach to basic statistical models including nonparametric density estimation, nonparametric regression, time series analysis including spectral analysis, filtering of time-continuous signals. Universal methods of estimation are proposed and a wide spectrum of applications of nonparametric methods is discussed. The topics range from survival analysis, measurement errors and binary and quantile regression to dependent errors, categorical data, bivariate time series, hidden components and learning machines. The emphasis is placed on small sample properties of the proposed data-driven orthogonal series estimates and on the graphical presentation of the methods. Asymptotic results, obtained via a filtering model, and other smoothing methods (kernel and spline estimation) are considered in separate chapters.
The very interesting and actual statistical topics together with the intuitive and informal style of presentation makes the book appealing to people entering this field, from graduate students to mature researchers. It is appropriate for a one-semester course for advanced undergraduate and graduate students of statistics, engeneering, medicine, business and social sciences. The prerequisites are intermediate calculus and introductory probability. Exercises of various levels, given at the end of each chapter, are useful for the instructor and for self-study.
The companion software package (available on the World Wide Web) allows the reader to produce and modify almost all figures of the book as well as to analyze simulated and real data sets. Based on the S-PLUS environment, this package requires no knowledge of S-PLUS and is elementary to use. This makes the material fully transparent and allows one to study interactively.
Reviewer: H.Liero (Potsdam)

MSC:

62G07 Density estimation
62-01 Introductory exposition (textbooks, tutorial papers, etc.) pertaining to statistics
62G08 Nonparametric regression and quantile regression
62M10 Time series, auto-correlation, regression, etc. in statistics (GARCH)

Software:

KernSmooth; R; S-PLUS
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