International Journal of Mathematics and Mathematical Sciences
Volume 2004 (2004), Issue 55, Pages 2947-2958

Large deviations for exchangeable observations with applications

Jinwen Chen

Department of Mathematical Sciences, Tsinghua University, Beijing 100084, China

Received 7 January 2003

Copyright © 2004 Jinwen Chen. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


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.