A class of nonparametric K-sample tests for semi-Markov counting processes

A K-sample testing problem is studied for multivariate semi-Markov counting processes. Asymptotic distributions and efficiency of a class of nonparame tric test statistics are established for certain local alternatives. The co ncept of the asymptotic efficiency stales that for every nonparametric test in this class, there is a parametric submodel for which the optimal test h as the same asymptotic power as the nonparametric test. The theory is illus trated by a simulation study and by analyzing the multivariate failure time data of Thompson et al. (1978).