Topics in non-parametric statistics. (English) Zbl 0998.62033

Emery, Michel et al., Lectures on probability theory and statistics. École d’Été de Probabilités de Saint-Flour XXVIII - 1998. Summer school, Saint-Flour, France, August 17 - September 3, 1998. Berlin: Springer. Lect. Notes Math. 1738, 85-277 (2000).
The subject of nonparametric statistics is statistical inference applied to noisy observations of infinite-dimensional “parameters”, like images and time-dependent signals. This is a mathematical area on the border between statistics and functional analysis, the latter name taken in its “literal” meaning – as geometry of spaces of functions. It would be impossible to outline in a short course the contents of the rich and highly developed area of nonparametric statistics; we restrict ourself to a number of selected topics related to estimating nonparametric regression functions and functionals of these functions. The presentation is self-contained, modulo a few facts from the theory of functional spaces. (From the preface.)
Contents: Ch. 1, Estimating regression functions from Hölder balls. Ch. 2, Estimating regression functions from Sobolev balls. Ch. 3, Spatial adaptive estimation on Sobolev balls. Ch. 4, Estimating signals satisfying differential inequalities. Ch. 5, Aggregation of estimates. I. Ch. 6, Aggregation of estimates. II. Ch. 7, Estimating functionals. I. Ch. 8, Estimating functionals. II.
For the entire collection see [Zbl 0941.00026].


62G08 Nonparametric regression and quantile regression
62-02 Research exposition (monographs, survey articles) pertaining to statistics
46N30 Applications of functional analysis in probability theory and statistics
62-01 Introductory exposition (textbooks, tutorial papers, etc.) pertaining to statistics