ar X iv : m at h / 06 04 19 7 v 2 [ m at h . PR ] 2 1 A pr 2 00 8 Two non - regular extensions of large deviation bound
نویسنده
چکیده
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 Rényi 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.
منابع مشابه
ar X iv : m at h / 06 04 19 7 v 1 [ m at h . PR ] 9 A pr 2 00 6 Two non - regular extensions of large deviation bound
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 Rényi entropies, we derive the...
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