Communications for Statistical Applications and Methods

The Korean Statistical Society (한국통계학회)
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The Minimum Squared Distance Estimator and the Minimum Density Power Divergence Estimator

  • Pak, Ro-Jin (Department of Information and Statistics, Dankook University)
  • Received : 20090900
  • Accepted : 20091000
  • Published : 2009.11.30
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Abstract

Basu et al. (1998) proposed the minimum divergence estimating method which is free from using the painful kernel density estimator. Their proposed class of density power divergences is indexed by a single parameter $\alpha$ which controls the trade-off between robustness and efficiency. In this article, (1) we introduce a new large class the minimum squared distance which includes from the minimum Hellinger distance to the minimum $L_2$ distance. We also show that under certain conditions both the minimum density power divergence estimator(MDPDE) and the minimum squared distance estimator(MSDE) are asymptotically equivalent and (2) in finite samples the MDPDE performs better than the MSDE in general but there are some cases where the MSDE performs better than the MDPDE when estimating a location parameter or a proportion of mixed distributions.

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References

  1. Basu, A., Harris, I. R., Jort, N. L. and Jones, M. C. (1998). Robust and effcient estimation by minimizing a density power divergence, Biometrika, 85, 549–559
  2. Beran, R. (1977). Minimum Hellinger distance estimators for parametric models, Annals of Statistics, 5, 445–463
  3. Silverman, B. W. (1986). Density Estimation for Statistics and Data Analysis, Chapman & Hall, London, 34–43
  4. Simpson, D. G. (1987). Minimum Hellinger distance estimation for the analysis of count data, Journal of the American Statistical Association, 82, 802–807
  5. Tamura, R. N. and Boos, D. D. (1986). Minimum Hellinger distance estimation for multivariate location and covariance, Journal of the American Statistical Association, 81, 223–229