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Sensitive parameters
Author(s) -
Tibshirani Robert,
Wasserman Larry A.
Publication year - 1988
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 - 10.2307/3314639.o
Subject(s) - mathematics , humanities , philosophy
Abstract Notions such as robustness and resistance of an estimator are well known and useful. These ideas have not been fully extended to functional parameters, although it seems natural to do so. In this paper we define a sensitive parameter as one for which small changes in the underlying distribution cause large changes in the parameter value. It is demonstrated that no nontrivial, nonparametric confidence procedure can exist for such a parameter. This extends a result of Bahadur and Savage ( 1956 ). The relationship between this definition and some standard concepts in robustness theory are explored, and implications for parametric inference are studied.