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\iteman{io-port 01183931}
\itemau{Dabrowska, Dorota M.}
\itemti{Weak convergence of a product integral dependence measure.}
\itemso{Scand. J. Stat. 23, No.4, 551-580 (1996).}
\itemab
Summary: 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 {\it P. Deheuvels}' [J. Multivariate Anal. 11, 102-113 (1981; Zbl 0486.62043)] decomposition of empirical copula functions into arrays of asymptotically independent Gaussian processes with distribution-free covariances. The one-to-one correspondence 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.
\itemrv{~}
\itemcc{}
\itemut{censoring; product integration; rank tests; survival functions}
\itemli{}
\end