On Inconsistent $M$-Estimators
Freedman, D. A. ; Diaconis, P.
Ann. Statist., Tome 10 (1982) no. 1, p. 454-461 / Harvested from Project Euclid
Text on Project Euclid
PDF
Alt PDF
If $M$ is not convex, and the underlying density is multi-modal, $M$-estimators can be inconsistent. Examples are given, as well as some positive results.
Publié le : 1982-06-14
Classification:  $M$-estimators,  $\psi$-functions,  robustness,  consistency,  62F35,  62E20 
@article{1176345786,
     author = {Freedman, D. A. and Diaconis, P.},
     title = {On Inconsistent $M$-Estimators},
     journal = {Ann. Statist.},
     volume = {10},
     number = {1},
     year = {1982},
     pages = { 454-461},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1176345786}
}

Freedman, D. A.; Diaconis, P. On Inconsistent $M$-Estimators. Ann. Statist., Tome 10 (1982) no. 1, pp.  454-461. http://gdmltest.u-ga.fr/item/1176345786/