Chapter 4 Nonparametric regression : minimax upper and lower bounds

We consider one of the two the most classical non-parametric problems in this example: estimating a regression function on a subset of the real line (the most classical problem being estimation of a density). In non-parametric regression, we assume there is an unknown function f : R → R, where f belongs to a pre-determined class of functions F ; usually this class is parameterized by some type of smoothness guarantee. To make our problems concrete, we will assume that the unknown function f is L-Lipschitz and defined on [0, 1]. Let F denote this class. (For a fuller technical introduction into nonparametric estimation, see the book by Tsybakov [2].)