Sankhya: The Indian Journal of Statistics

1993, Volume 55, Series B, Pt. 1, 48-56

ROBUST $M$-ESTIMATION OF LOCATION DIFFERENCE IN TYPE II CENSORED SAMPLES

By

INDRANI BASAK, Pennsylvania State University at Altoona

 

SUMMARY. The conventional way of robust estimation of the location differnces is by taking the difference of the robust estimates of two locations. The optimal member of this class will be referred to as usual optimal robust estimators. An alternative robust M-estimator of the location difference is derived using the Neyman-Scott parameterization; the estimators corresponding to the optimal members will be referred to as new optimal robust estimators. The James-type new optimal robust estimators are the new optimal robust estimators pertaining to a restricted class of Y - functions which is analogue of the class of Y - functions considered in James (1986)m for randomly censored data. The usual optimal robust estimators have breakdown point less than 0.5 as is shown particularly for extreme value distribution. It is shown that the James type new optimal robust estimators have breakdown point 0.5 when the amounts of censoring for each sample are less than 50% even when the underlying distribution is not symmetric. Moreover these new optimal robust estimators do not compromise the asymptotic efficiency with the usual optimal robust estimators.

AMS(1980)subject classification. 62F35,62N05

Key words and phrases. Asymptotic efficiency, breakdown points, Neyman-scott parametrization, optimal robust estimators, random censoring

FULL PAPER.

This article in Mathematical Reviews.