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Biometrika 1998 85(3):549-559; doi:10.1093/biomet/85.3.549
© 1998 by Biometrika Trust
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Robust and efficient estimation by minimising a density power divergence

AYANENDRANATH BASU, IAN R. HARRIS, NILS L. HJORT and M. C. JONES

Applied Statistics Unit, Indian Statistical Institute 203 Barrackpore Trunk Road, Calcutta 700 035, Indiaayanbasu{at}isical.ernet.in
Department of Mathematics, Northern Arizona University Flagstaff Arizona 86011, U.S.A.irh{at}odin.math.nau.edu
Department of Mathematics and Statistics, University of Oslo P.B. 1053 Blindern, N-0316 Oslo, Norwaynils{at}math.uio.no
Department of Statistics, The Open University Milton Keynes, MK7 6AA, U.K.m.c.jones{at}open.ac.uk

A minimum divergence estimation method is developed for robust parameter estimation. The proposed approach uses new density-based divergences which, unlike existing methods of this type such as minimum Hellinger distance estimation, avoid the use of nonparametric density estimation and associated complications such as bandwidth selection. The proposed class of ‘density power divergences’ is indexed by a single parameter {alpha} which controls the trade-off between robustness and efficiency. The methodology affords a robust extension of maximum likelihood estimation for which {alpha} = 0. Choices of {alpha} near zero afford considerable robustness while retaining efficiency close to that of maximum likelihood.

Key Words: Asymptotic efficiency • Influence function • M-estimation • Maximum likelihood • Minimum distance estimation • Robustness


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