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Efficient bias‐Robust M‐Estimators of location in Kolmogorov normal neighbourhoods
Author(s) -
Wu Eden K.H.,
Zhou Julie
Publication year - 1998
Publication title -
canadian journal of statistics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.804
H-Index - 51
eISSN - 1708-945X
pISSN - 0319-5724
DOI - 10.2307/3315509
Subject(s) - estimator , neighbourhood (mathematics) , mathematics , efficiency , minimax , gaussian , statistics , normal distribution , mathematical analysis , mathematical optimization , physics , quantum mechanics
We consider minimax‐bias M‐estimation of a location parameter in a Kolmogorov neighbourhood K () of a normal distribution. The maximum asymptotic bias of M‐estimators for the Kolmogorov normal neighbourhood is derived, and its relation with the gross‐error sensitivity of the estimator at the nominal model (the Gaussian case) is found. In addition, efficient bias‐robust M‐estimators T i are constructed. Numerical results are also obtained to show the percentage of increase in maximum asymptotic bias and the efficiency we can achieve for some well‐known ‐functions.