Nonparametric tests for multiple regression under progressive censoring

For continuous observations from time-sequential studies, suitable Cramér-von Mises and Kolmogorov-Smirnov types of (nonparametric) statistics (based on linear rank statistics) for testing hypotheses on some multiple-regression models are proposed and studied. The asymptotic theory of these tests is provided for both the null and (local) alternative hypotheses situations and is based on the weak convergence of suitable rank order processes (on the D[0, 1] space) to certain functions of Brownian motions. Bahadur efficiency results are also presented. Empirical values of the percentile points of the null distributions of the proposed test statistics, obtained through simulation studies, are also provided.