The Pure and Applied Mathematics (한국수학교육학회지시리즈B:순수및응용수학)
- Volume 9 Issue 1
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- Pages.81-90
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- 2002
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- 1226-0657(pISSN)
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- 2287-6081(eISSN)
ROBUST $L_{p}$ -NORM ESTIMATORS OF MULTIVARIATE LOCATION IN MODELS WITH A BOUNDED VARIANCE
- Georgly L. Shevlyakov (Department of Mathematics, St. Petersburg State Technical University) ;
- Lee, Jae-Won (Department of Applied Mathematics, School of Natural Sciences, Kumoh National University Of Technology)
- Published : 2002.05.01
Abstract
The least informative (favorable) distributions, minimizing Fisher information for a multivariate location parameter, are derived in the parametric class of the exponential-power spherically symmetric distributions under the following characterizing restrictions; (i) a bounded variance, (ii) a bounded value of a density at the center of symmetry, and (iii) the intersection of these restrictions. In the first two cases, (i) and (ii) respectively, the least informative distributions are the Gaussian and Laplace, respectively. In the latter case (iii) the optimal solution has three branches, with relatively small variances it is the Gaussian, them with intermediate variances. The corresponding robust minimax M-estimators of location are given by the
Keywords
- Robust estimation;
- minimax M-estimators;
- multivariate location;
- $L_{p}$-norm method;
- adaptive estimation