On sharp nonparametric estimation of differentiable functions

Sam Efromovich

Statistics & Probability Letters, 2019, vol. 152, issue C, 9-14

Abstract: Sharp minimax nonparametric estimation is well known for functions from a Sobolev ellipsoid which is defined via Fourier coefficients of differentiable functions with specific boundary conditions. The theory is based on a renown lower bound of Pinsker (1980) and an adaptive estimator that attains it. This paper solves a long-standing problem of adaptive estimation without assuming boundary conditions.

Keywords: Adaptation; Filtration; Pinsker’s lower bound; Minimax (search for similar items in EconPapers)
Date: 2019
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Citations: View citations in EconPapers (1)

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DOI: 10.1016/j.spl.2019.04.007

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