Masahito Hayashi
Published 2006-04-09, updated 2008-04-21Version 2
We formulate two types of extensions of the large deviation theory initiated by Bahadur in a non-regular setting. One can be regarded as a bound of the point estimation, the other can be regarded as the limit of a bound of the interval estimation. Both coincide in the regular case, but do not necessarily coincide in a non-regular case. Using the limits of relative R\'{e}nyi entropies, we derive their upper bounds and give a necessary and sufficient condition for the coincidence of the two upper bounds. We also discuss the attainability of these two bounds in several non-regular location shift families.
Comments: This manusript is shortened version of the previouse manuscript
Two non-regular extensions of the large deviation bound
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