Statistica Sinica 9(1999), 211-227

A CLASS OF NONPARAMETRIC K-SAMPLE TESTS FOR

SEMI-MARKOV COUNTING PROCESSES

I-Shou Chang, Yuan-Chuan Chuang and Chao A. Hsiung^*

National Central University, Ming-Chuan University and

^*National Health Research Institute and Academia Sinica

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.