For a particular pseudoloss function, local asymptotic minimaxity and admissibility in the sense of Hajek and Le Cam are studied when probability measures are replaced by certain capacities ($\epsilon$-contamination, total variation). A minimax bound for arbitrary estimator sequences is established, admissibility of minimax estimators is proved, and it is shown that minimax estimators must necessarily have an asymptotic expansion in terms of a truncated logarithmic derivative.
Publié le : 1981-03-14
Classification:
Local asymptotic minimax bound,
local asymptotic admissibility,
asymptotic expansions,
regular estimators,
superefficiency,
contiguity,
least favorable pairs,
62G35,
62E20,
62C15
@article{1176345393,
author = {Rieder, Helmut},
title = {On Local Asymptotic Minimaxity and Admissibility in Robust Estimation},
journal = {Ann. Statist.},
volume = {9},
number = {1},
year = {1981},
pages = { 266-277},
language = {en},
url = {http://dml.mathdoc.fr/item/1176345393}
}
Rieder, Helmut. On Local Asymptotic Minimaxity and Admissibility in Robust Estimation. Ann. Statist., Tome 9 (1981) no. 1, pp. 266-277. http://gdmltest.u-ga.fr/item/1176345393/