Most Economical Robust Selection Procedures for Location Parameters
Dalal, S. R. ; Hall, W. J.
Ann. Statist., Tome 7 (1979) no. 1, p. 1321-1328 / Harvested from Project Euclid
Consider samples of size $n$ from each of $k$ symmetric populations, differing only in their location parameters. The decision problem is to select the best population--the one with the largest location parameter--with control on the probability of correct selection (PCS) whenever the largest parameter is at least $\Delta$ units larger than all others, and whenever the common error distribution belongs to a specified neighborhood of the standard normal. It is shown that, if the sample size $n$ is chosen according to a formula given herein, and Huber's $M$-estimate is applied to each of the $k$ samples with the population having the largest estimate being selected as best, that the PCS goal is achieved asymptotically (as $\Delta\downarrow 0$)--the procedure is robust. Moreover, no other selection procedure can achieve this goal asymptotically with a smaller sample size--the procedure is most economical. Comparisons with other procedures are given. These results are based on a uniform asymptotic normality theorem for Huber's $M$-estimate, contained herein.
Publié le : 1979-11-14
Classification:  Selection procedures,  robust procedures,  Huber's $M$-estimate,  location parameters,  uniform asymptotic normality,  62F07,  62G35
@article{1176344849,
     author = {Dalal, S. R. and Hall, W. J.},
     title = {Most Economical Robust Selection Procedures for Location Parameters},
     journal = {Ann. Statist.},
     volume = {7},
     number = {1},
     year = {1979},
     pages = { 1321-1328},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1176344849}
}
Dalal, S. R.; Hall, W. J. Most Economical Robust Selection Procedures for Location Parameters. Ann. Statist., Tome 7 (1979) no. 1, pp.  1321-1328. http://gdmltest.u-ga.fr/item/1176344849/