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LOSS OF INFORMATION ASSOCIATED WITH THE ORDER STATISTICS AND RELATED ESTIMATORS IN THE DOUBLE EXPONENTIAL DISTRIBUTION CASE |
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| Authors: | Masafumi Akahira Kei Takeuchi |
| Affiliation: | University of Tsukuba and University of Tokyo;Institute of Mathematics, University of Tsukuba, Ibaraki 305, Japan;Research Center for Advanced Science and Technology, University of Tokyo, 4–6-1 Komaba, Meguro-ku, Tokyo 156, Japan |
| Abstract: | 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. |
| Keywords: | Loss of information double exponential distribution second order asymptotic efficiency maximum likelihood estimator median |