Order-Restricted Inference with Linear Rank Statistics in Microarray Data

The classification of subjects with unknown distribution in a small sample size often involves order-restricted constraints in multivariate parameter setups. Those problems make the optimality of a conventional likelihood ratio based statistical inferences not feasible. Fortunately, Roy (1953) introduced union-intersection principle(UIP) which provides an alternative avenue. Multivariate linear rank statistics along with that principle, yield a considerably appropriate robust testing procedure. Furthermore, conditionally distribution-free test based upon exact permutation theory is used to generate p-values, even in a small sample. Applications of this method are illustrated in a real microarray data example (Lobenhofer et al., 2002).