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Introduction to nonparametric estimation. (Introduction à l’estimation non-paramétrique.) (French) Zbl 1029.62034
Mathématiques & Applications (Berlin). 41. Paris: Springer. x, 175 p. (2004).
This monograph provides a concise introduction to nonparametric curve estimation for independent data. In its three chapters the author first introduces some of the most prominent estimators (kernel, local polynomial, series) for a density and a regression function. The third model discussed is the Gaussian shift model. The main focus of Chapter One is on the pointwise and global tradeoff between bias and variance and how to minimize the overall error. Chapter Two discusses the problem how to find minimax estimators for densities and regression functions. Finally, in Chapter Three, adaptive estimation (in the minimax sense) is dealt with in the context of the normal shift model (Pinsker’s Theorem).
Summarizing, this booklet provides a compact technical introduction to the subject. A discussion from a data analytic point of view is missing.
Reviewer: W.Stute (Gießen)

62G07 Density estimation
62-01 Introductory exposition (textbooks, tutorial papers, etc.) pertaining to statistics
62G08 Nonparametric regression and quantile regression