Graduate Thesis Or Dissertation
 

Non parametric c-sample tests for arbitrarily censored data

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  • Consider the c- sample testing problem with null hypothesis H[subscript]o : F₁(x) = ... = F[subscript]c(x), where F[subscript]j(x), j = 1 ..., c, represent absolutely continuous distribution functions for failure distributions. Furthermore, consider arbitrarily (right) censored samples, which may arise from putting the (censored) experimental units on test at different times. The c-sample test that we shall be primarily concerned with is an extension of a generalized Savage test proposed by Thomas [25] for the two-sample case. This c-sample test statistic, Q[subscript](r,N)' is shown to have an asymptotic chi- square distribution under H[subscript]o and an asymptotic non-central chi-square distribution locally under alternatives with proportional hazard functions. The Q[subscript](r,N) statistic is shown to give an asymptotic efficient test with respect to the likelihood ratio test for exponential failure distributions with exponential censoring distributions. Conditional small sample power comparisons of Q[subscript](r,N) are also made with a c-sample extension of Gehan's [11] two-sample Wilcoxon type statistic.
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