LARGE DEVIATIONS FOR EXCHANGEABLE RANDOM VECTORS

• 成果类型: Article
• 署名作者: DINWOODIE, IH; ZABELL, SL
• 刊物名称: ANNALS OF PROBABILITY
• ISSN/ISSBN: 0091-1798
• DOI: 10.1214/aop/1176989683
• 发表日期: 1992
• 页码: 1147-1166
• 关键词: probability; SPACES

摘要

Say that a family (P(theta)n: theta is-an-element-of THETA) of sequences of probability measures is exponentially continuous if whenever theta(n) --> theta, the sequence {P(theta-n)n} satisfies a large deviation principle with rate function lambda(theta). If THETA is compact and {P(theta)n} is exponentially continuous, then the mixture P(n)(A) =: integral-THETA P(theta)n(A)d-mu(theta) satisfies a large deviation principle with rate function lambda(x) =: inf{lambda(theta)(x): theta is-an-element-of S(mu)}, where S(mu) is the support of the mixing measure mu. If X1, X2,... is a sequence of i.i.d. random vectors, {X(n)BAR} the corresponding sequence of sample means and P(theta)n =: P(theta)-degrees X(n)-1BAR then {P(theta)n} is exponentially continuous if the classical rate function lambda(theta)(upsilon) 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-THETA 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.