Inadmissibility of robust estimators with respect to \(L_1\) norm. (English) Zbl 0933.62007
Dodge, Yadolah (ed.), \(L_1\)-statistical procedures and related topics. Papers of the 3rd international conference on \(L_1\) norm and related methods held in Neuchâtel, Switzerland, August 11–15, 1997. Hayward, CA: IMS, Institute of Mathematical Statistics. IMS Lect. Notes, Monogr. Ser. 31, 71-78 (1997).
Summary: We show that robust \(M\)-estimators as well as equivariant estimators which do not depend on the extreme observations are inadmissible estimators of the location with respect to the \(L_1\) loss function for a broad class of distributions. As a consequence, it implies that the sample median is inadmissible as an estimator of the location of the double-exponential distribution.
For the entire collection see [Zbl 0882.00044].
For the entire collection see [Zbl 0882.00044].
MSC:
| 62C15 | Admissibility in statistical decision theory |
| 62F35 | Robustness and adaptive procedures (parametric inference) |
