International Journal of Mathematics and Mathematical Sciences
Volume 2004 (2004), Issue 53-56, Pages 2947-2958
doi:10.1155/S0161171204301444

Large deviations for exchangeable observations with applications

Abstract

We first prove some large deviation results for a mixture of i.i.d. random variables. Compared with most of the known results in the literature, our results are built on relaxing some restrictive conditions that may not be easy to be checked in certain typical cases. The main feature in our main results is that we require little knowledge of (continuity of) the component measures and/or of the compactness of the support of the mixing measure. Instead, we pose certain moment conditions, which may be more practical in applications. We then use the large deviation approach to study the problem of estimating the component and the mixing measures.