Two non-regular extensions of large deviation bound

Details Two non-regular extensions of large deviation bound Two non-regular extensions of large deviation bound

2006-04-09

arxiv.org/abs/math/0604197v2

Mathematics

Probability

This manusript is shortened version of the previouse manuscript

Scientific paper

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.

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