

























This paper presents a multivariate normal integral representation for the joint survival function of the cumulative sums of the components of any multinomial random vector at interior lattice points. This result can be viewed as a multivariate analog of Equation (7) in Carter and Pollard (2004), whose proof starts from the beta integral representation of binomial survival probabilities and uses Laplace's method to improve Tusnády's inequality. Our findings are based on a crucial relationship between the joint survival function of the cumulative sums of the components of any multinomial random vector and a Dirichlet probability over a corresponding cumulative-sum region. The main motivation is that such an explicit formula may eventually help streamline the conditional quantile-transformation arguments used in the multivariate KMT approximation of Einmahl (1989), a connection left for future work. We provide numerical checks of the identity for $d = 2,3,4,5$.
此内容由惯性聚合(RSS阅读器)自动聚合整理,仅供阅读参考。 原文来自 — 版权归原作者所有。