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LOSS OF INFORMATION OF A STATISTIC FOR

A FAMILY OF NON-REGULAR DISTRIBUTIONS

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MASAFUMI AKAHIRA

*Institute of Mathematics, University of Tsukuba, Ibaraki 305,
Japan*
(Received January 28, 1994; revised April 10, 1995)

**Abstract.**
In the non-regular case, the asymptotic loss of
amount of information (extended to as Rényi 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.

*Key words and phrases*:
Amount of Rényi type
information, loss of information, non-regular case, extreme
statistics, asymptotically ancillary statistic, truncated
distributions.

**Source**
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