OPTIMAL 2ND-ORDER PRODUCT PROBABILITY BOUNDS

Let P(c) = P(X1 less-than-or-equal-to c1, ... ,X(p) less-than-or-equal -to c(p)) for a random vector (X1, . . . ,X(p)). Bounds are considered of the form [GRAPHICS] where T is a spanning tree corresponding to th e bivariate probability structure and d(i) is the degree of the vertex i in T. An optimized version of this inequality is obtained. The main result is that beta2T(c) always dominates certain second-order Bonfer roni bounds. Conditions on the covariance matrix of a N(0, SIGMA) dist ribution are given so that this bound applies, and various application s are given. AMS 1991 SUBJECT CLASSIFICATION: PRIMARY 62 H05