Smoothing techniques. With implementation in S. (English) Zbl 0716.62040

Härdle, Wolfgang

Springer Series in Statistics. New York etc.: Springer-Verlag. xi, 261 p. DM 78.00 (1991).

The aim of the book is to provide a non-technical introduction into the area of smoothing techniques in statistics. Based on a representation of well-known results from the theory of nonparametric density and regression function estimation the application of these methods in the modern computing environment S is discussed. The computational aspects of the estimation algorithms are described in great detail, their implementation in S is included. A main aspect in the text is to present a highly effective algorithm for the solution of the problem of data sparseness in the case of smoothing in high dimensions. For this purpose the author develops a so-called WARPing (Weighted Averaging using Rounded Points)-method, which is based on discretizing the data first into a finite grid of bins and then smoothing the binned data.
Since the author has put emphasis on the practical realization of the results coming from the theory of smoothing, the book is recommended in particular to statisticians leaning more towards applied aspects. The text is written at the introductory level and can be used in undergraduate teaching. Each chapter is completed by exercises (with solutions).

Reviewer: H.Liero

MSC:

62G07	Density estimation
62-01	Introductory exposition (textbooks, tutorial papers, etc.) pertaining to statistics
62-07	Data analysis (statistics) (MSC2010)
62-04	Software, source code, etc. for problems pertaining to statistics
65C99	Probabilistic methods, stochastic differential equations
62G35	Nonparametric robustness
65D10	Numerical smoothing, curve fitting

Keywords:

bandwidth selection; histogram; kernel estimation; density estimation; nonparametric regression; S-interactive computing environment; WARPing algorithm; smoothing techniques; estimation algorithms; implementation in S; data sparseness; smoothing in high dimensions; Weighted Averaging using Rounded Points; exercises; solutions

Software:

alr3