WEAK-CONVERGENCE OF A PRODUCT INTEGRAL DEPENDENCE MEASURE

ySome properties of a product integral representation of multivariate survival functions are discussed. It provides a decomposition of a sur vival function in terms of signed interaction measures. It is shown th at a censored data sample analogue of this decomposition is asymptotic ally Gaussian. Under the null hypothesis of mutual independence of the failure times the limiting process is given by an array of independen t Brownian motions with variance functions which ran be easily estimat ed from censored data. The result generalizes to censored data Deheuve ls' (1981) decomposition of empirical copula functions into array of a symptotically independent Gaussian processes with distribution-free co variances. The one-to-one correspondence of this decomposition with sc ores of censored data rank statistics for mutual independence is also discussed and a new class of independence tests for multivariate data proposed.