Open Access
November 2014 Minimax bounds for estimation of normal mixtures
Arlene K.H. Kim
Bernoulli 20(4): 1802-1818 (November 2014). DOI: 10.3150/13-BEJ542


This paper deals with minimax rates of convergence for estimation of density functions on the real line. The densities are assumed to be location mixtures of normals, a global regularity requirement that creates subtle difficulties for the application of standard minimax lower bound methods. Using novel Fourier and Hermite polynomial techniques, we determine the minimax optimal rate – slightly larger than the parametric rate – under squared error loss. For Hellinger loss, we provide a minimax lower bound using ideas modified from the squared error loss case.


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Arlene K.H. Kim. "Minimax bounds for estimation of normal mixtures." Bernoulli 20 (4) 1802 - 1818, November 2014.


Published: November 2014
First available in Project Euclid: 19 September 2014

zbMATH: 1320.62082
MathSciNet: MR3263090
Digital Object Identifier: 10.3150/13-BEJ542

Keywords: Assouad’s lemma , Hermite polynomials , minimax lower bound , normal location mixture

Rights: Copyright © 2014 Bernoulli Society for Mathematical Statistics and Probability

Vol.20 • No. 4 • November 2014
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