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LOSS OF INFORMATION ASSOCIATED WITH THE ORDER STATISTICS AND RELATED ESTIMATORS IN THE DOUBLE EXPONENTIAL DISTRIBUTION CASE
Author(s) -
Akahira Masafumi,
Takeuchi Kei
Publication year - 1990
Publication title -
australian journal of statistics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.434
H-Index - 41
eISSN - 1467-842X
pISSN - 0004-9581
DOI - 10.1111/j.1467-842x.1990.tb01024.x
Subject(s) - estimator , mathematics , statistics , order statistic , exponential distribution , exponential function , fisher information , exponential family , maximum likelihood , distribution (mathematics) , order (exchange) , asymptotic distribution , mathematical analysis , finance , economics
Summary Fisher (1934) derived the loss of information of the maximum likelihood estimator (MLE) of the location parameter in the case of the double exponential distribution. Takeuchi & Akahira (1976) showed that the MLE is not second order asymptotically efficient. This paper extends these results by obtaining the (asymptotic) losses of information of order statistics and related estimators, and by comparing them via their asymptotic distributions up to the second order.