Large Deviations for Exchangeable Random Vectors

satisfies a large deviation principle with rate function A(x)= inf{A6(x): o E S(,u)1, where S(4) is the support of the mixing measure 4. If X1, X2,.. . is a sequence of i.i.d. random vectors, {Xn} the corresponding sequence of sample means and Pown =: Po X1, then {Pon} is exponentially continuous if the classical rate function AR(v) is jointly lower semicontinuous and a uniform integrability condition introduced by de Acosta is satisfied. These results are applied in Section 4 to derive a large deviation theory for exchangeable random variables; the resulting rate functions are typically nonconvex. If the parameter space e is not compact, then examples can be constructed where a full large deviation principle is not satisfied because the upper bound fails for a noncompact set.