A Counterexample on Translation Invariant Estimators
Torgersen, Erik N.
Ann. Math. Statist., Tome 42 (1971) no. 6, p. 1450-1451 / Harvested from Project Euclid
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It seems to be generally known that the proof of the continuity part of Theorem 1 in Hodges' and Lehmann's paper (1963) is incorrect. The fact that the theorem is incorrect is--perhaps--not so well known. We show this by constructing independent real random variables $X_1,\cdots, X_n$, each having the same non-atomic symmetric distribution, and an odd translation invariant estimator $h(X_1,\cdots, X_n)$ such that $P(h(X_1,\cdots, X_n) = 0) > 0. h$ may be chosen symmetric provided $n \geqq 3$.
Publié le : 1971-08-14
Classification:  
@article{1177693260,
     author = {Torgersen, Erik N.},
     title = {A Counterexample on Translation Invariant Estimators},
     journal = {Ann. Math. Statist.},
     volume = {42},
     number = {6},
     year = {1971},
     pages = { 1450-1451},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1177693260}
}

Torgersen, Erik N. A Counterexample on Translation Invariant Estimators. Ann. Math. Statist., Tome 42 (1971) no. 6, pp.  1450-1451. http://gdmltest.u-ga.fr/item/1177693260/