Abstract: A K-sample testing problem is studied for multivariate semi-Markov count ing processes. Asymptotic distributions and efficiency of a class of nonparametric test statis tics are established for certain local alternatives. The concept of the asymptotic efficiency states that for every nonparametric test in this class, there is a parametric submodel for which the optimal test has the same asymptotic power as the nonparametric test. The theory is illustrated by a simulation study and by analyzing the multivariate failure time data of Thompson et al. (1978).
Key words and phrases: Asymptotic distribution, asymptotic efficiency, K-sample test, parametric submodel, semi-Markov counting process.