Weak Convergence of a Product Integral Dependence Measure
研究了多元生存函数的乘积积分表示及其性质，证明了该分解的删失数据样本渐近服从高斯分布，并基于此提出了一类新的多元独立性检验方法。
Some properties of a product integral representation of multivariate survival functions are discussed. It provides a decomposition of a survival function in terms of signed interaction measures. It is shown that a censored data sample analogue of this decomposition is asymptotically Gaussian. Under the null hypothesis of mutual independence of the failure times the limiting process is given by an array of independent Brownian motions with variance functions which can be easily estimated from censored data. The result generalizes to censored data Deheuvels' (1981) decomposition of empirical copula functions into array of asymptotically independent Gaussian processes with distribution-free covariances. The one-to-one correspon- dence of this decomposition with scores of censored data rank statistics for mutual independence is also discussed and a new class of independence tests for multivariate data proposed.