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On the relation between Hodges‐Lehmann efficiency and Pitman efficiency
Author(s) -
Kourouklis Stavros
Publication year - 1989
Publication title -
canadian journal of statistics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.804
H-Index - 51
eISSN - 1708-945X
pISSN - 0319-5724
DOI - 10.2307/3315526
Subject(s) - relation (database) , mathematics , context (archaeology) , estimator , independent and identically distributed random variables , equivalence (formal languages) , efficiency , statistics , mathematical economics , econometrics , computer science , discrete mathematics , geography , random variable , data mining , archaeology
The relation between Hodges–Lehmann efficiency and Pitman efficiency is studied in the context of testing one‐sided hypotheses about a real‐valued parameter. It is first shown that for tests based on sums of independently and identically distributed observations local Hodges‐Lehmann efficiency is equivalent to Pitman efficiency. Then, it is proved that this equivalence also carries over to tests based on two broad classes of M ‐estimators for the location problem. In all cases considered explicit formulas of the Hodges‐Lehmann efficacies are obtained.