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L p –Estimators as Estimates of a Parameter of Location for a Sharp–pointed Symmetric Density
Author(s) -
Arcones Miguel A.
Publication year - 1998
Publication title -
scandinavian journal of statistics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.359
H-Index - 65
eISSN - 1467-9469
pISSN - 0303-6898
DOI - 10.1111/1467-9469.00130
Subject(s) - mathematics , estimator , gaussian , location parameter , limit (mathematics) , euclidean distance , distribution (mathematics) , mathematical analysis , m estimator , euclidean geometry , combinatorics , statistics , geometry , physics , quantum mechanics
We study the asymptotics of L p estimators, p > 0, over a sample having a symmetric density with a sharp–point at the centre of symmetry of the distribution. The rates of convergence of the L p estimators in this situation depend on p and on the shape of the density. To obtain some of the limit distributions, we present new results in the asymptotics of M–estimators. We extend the delta method to the case when the Euclidean norm of the conveniently normalized M–estimators converge to a power of the Euclidean norm of a (possibly Gaussian) stable distribution.