Two non-regular extensions of the large deviation bound
Probability
2007-06-13 v1 Statistics Theory
Statistics Theory
Abstract
We formulate two types of extension 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 Renyi entropies, we derive their upper bounds and give a necessary and sufficient condition for the coincidence of the two upper bounds. We also show the attainability of these two bounds in several non-regular location shift families.
Cite
@article{arxiv.math/0212076,
title = {Two non-regular extensions of the large deviation bound},
author = {Masahito Hayashi},
journal= {arXiv preprint arXiv:math/0212076},
year = {2007}
}