Robust inference with order constraint in microarray study

Gene classification can involve complex order-restricted inference. Examining gene expression pattern across groups with order-restriction makes standard statistical inference ineffective and thus, requires different methods. For this problem, Roy's union-intersection principle has some merit. The M-estimator adjusting for outlier arrays in a microarray study produces a robust test statistic with distribution-insensitive clustering of genes. The M-estimator in conjunction with a union-intersection principle provides a nonstandard robust procedure. By exact permutation distribution theory, a conditionally distribution-free test based on the proposed test statistic generates corresponding p-values in a small sample size setup. We apply a false discovery rate (FDR) as a multiple testing procedure to p-values in simulated data and real microarray data. FDR procedure for proposed test statistics controls the FDR at all levels of ${\alpha}$ and ${\pi}_0$ (the proportion of true null); however, the FDR procedure for test statistics based upon normal theory (ANOVA) fails to control FDR.