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| Titel: |
Maximum asymptotic variances of mndash;estimators of location with auxiliary scale estimator under symmetric contamination |
| Auteur: |
Wong, H. Y. Su |
| Verschenen in: |
Communications in statistics |
| Paginering: | Jaargang 21 (1992) nr. 3 pagina's 783-805 |
| Jaar: |
1992 |
| Inhoud: |
The model for the error distribution is [image omitted] , where F0 is a known distribution symmetric about 0, ε is a fixed proportion of contamination, and G is an unknown symmetric distribution. The two auxiliary scale estimators are "Huber proposal 2" estimator [image omitted] and interquantile range of sample distribution [d](F). In "Huber proposal 2" case, we first obtain the breakdown points for the estimator and also the range :[image omitted] of [image omitted] . For each fixed [image omitted] , the maximum asymptotic variance [image omitted] subject to [image omitted] is obtained by putting some of the contaminating mass at 0 and the rest of mass at [d] [d]. The original infinite-dimensional problem is then reduced to a one-dimensional problem of finding the value of [d] for which V([d]) is maximized. The result obtained is that this maximum is always attained at [d]max. When ψ is monotone and the scale estimator is S(F), for fixed [image omitted] , the maximum variance V(s) subject to S(F) = s is attained by placing the contaminating mass at [image omitted] . A sufficient condition under which V(s) is maximized at Smaxis given. However, the asymptotic variance is not always maximized at Smax even for monotone ψ. |
| Uitgever: |
Taylor & Francis |
| Bronbestand: |
Elektronische Wetenschappelijke Tijdschriften |
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