Lower Bounds for Function Estimation

Catherine Huber
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Catherine Huber: Université Paris V

Chapter 15 in Festschrift for Lucien Le Cam, 1997, pp 245-258 from Springer

Abstract: Abstract Over the last thirty years, it has been recognized that a common abstract framework underlies many basic problems of nonparametric estimation. In that framework, f is an unknown function to be estimated, known to belong to a class.P of smooth functions, and an observation X is available in order to perform the estimation. The X has its values in a measurable space (E,13) and obeys a probability law indexed by f and denoted Pf. The set of all probabilities P 9 where g varies in.P is denoted P.

Keywords: Function Estimation; Optimal Rate; SOBOLEV Class; Hellinger Distance; Orthogonal Series (search for similar items in EconPapers)
Date: 1997
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DOI: 10.1007/978-1-4612-1880-7_15

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