Introduction to Nonparametric Estimation

Abstract

My reaction on seeing the title of this book was ‘Nonparametric estimation of what?’. The answer is densities, regression functions and some closely related concepts such as Gaussian white noise models. As is often the case ‘Introduction to’ in the title may be interpreted here as ‘a fairly advanced treatment of’. The book is an updated translation of a French version that was published in 2003 and is based on lecture notes for a postgraduate course.Owing to the nature of their training and work demands applied statisticians often do not have the mathematical background or time to cope easily with the advanced mathematics that are needed by, or at any rate used by, many theoretical statisticians. Do not expect to master this book if you are not happy with things like Lebesgue measures, Borel sets or understanding formidable equations or formulae. For example, there are many cases in this book where one symbol such as f appears in the same formula or equation both with and without different appendages like subscripts, superscripts or a ‘hat’ and is sometimes itself even used as a subscript.