Pathologies of some Minimum Distance Estimators
Donoho, David L. ; Liu, Richard C.
Ann. Statist., Tome 16 (1988) no. 1, p. 587-608 / Harvested from Project Euclid
Text on Project Euclid
PDF
Alt PDF
Minimum distance estimates are studied at the $N(\theta, 1)$ model. Estimates based on a non-Hilbertian distance $\mu (\mu = \text{Kolmogorov-Smirnov, Levy, Kuiper, variation and Prohorov})$ can exhibit very large variances, or even outright inconsistency, at distributions arbitrarily close to the model in terms of $\mu$-distance. For Hilbertian distances $(\mu = \text{Cramer-von Mises, Hellinger})$ this problem does not seem to occur. Geometric motivation for these results is provided.
Publié le : 1988-06-14
Classification:  Inconsistency,  Hadamard and Frechet differentiability of statistical functionals,  62F35,  62F12 
@article{1176350821,
     author = {Donoho, David L. and Liu, Richard C.},
     title = {Pathologies of some Minimum Distance Estimators},
     journal = {Ann. Statist.},
     volume = {16},
     number = {1},
     year = {1988},
     pages = { 587-608},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1176350821}
}

Donoho, David L.; Liu, Richard C. Pathologies of some Minimum Distance Estimators. Ann. Statist., Tome 16 (1988) no. 1, pp.  587-608. http://gdmltest.u-ga.fr/item/1176350821/