Loss of information of a statistic for a family of non-regular distributions

✍ Scribed by Masafumi Akahira

• Book ID: 104624002
• Publisher: Springer Japan
• Year: 1996
• Tongue: English
• Weight: 578 KB
• Volume: 48
• Category: Article
• ISSN: 0020-3157
• DOI: 10.1007/bf00054795

✦ Synopsis

In the non-regular case, the asymptotic loss of amount of information (extended to as R~nyi measure) associated with a statistic is discussed. It is shown that the second order asymptotic loss of information in reducing to a statistic consisting of extreme values and an asymptotically ancillary statistic vanishes. This result corresponds to the fact that the statistic is second order asymptotically sufficient in the sense of Akahira (1991, Metron, 49, 133 143). Some examples on truncated distributions are also given.