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Estimator Selection: a New Method with Applications to Kernel Density Estimation

Claire Lacour (claire.lacour@u-psud.fr), Pascal Massart (pascal.massart@u-psud.fr) and Vincent Rivoirard (rivoirard@ceremade.dauphine.fr)
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Claire Lacour: University Paris-Sud
Pascal Massart: University Paris-Sud
Vincent Rivoirard: Université Paris Dauphine

Sankhya A: The Indian Journal of Statistics, 2017, vol. 79, issue 2, No 7, 298-335

Abstract: Abstract Estimator selection has become a crucial issue in non parametric estimation. Two widely used methods are penalized empirical risk minimization (such as penalized log-likelihood estimation) or pairwise comparison (such as Lepski’s method). Our aim in this paper is twofold. First we explain some general ideas about the calibration issue of estimator selection methods. We review some known results, putting the emphasis on the concept of minimal penalty which is helpful to design data-driven selection criteria. Secondly we present a new method for bandwidth selection within the framework of kernel density density estimation which is in some sense intermediate between these two main methods mentioned above. We provide some theoretical results which lead to some fully data-driven selection strategy.

Keywords: Concentration inequalities; Kernel density estimation; Penalization methods; Estimator selection; Oracle inequality; Primary: 62G05; Secondary: 62C20; 62H12. (search for similar items in EconPapers)
Date: 2017
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Citations: View citations in EconPapers (8)

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DOI: 10.1007/s13171-017-0107-5

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