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Robust inference with order constraint in microarray study
Commun. Stat. Appl. Methods, CSAM 2018;25:559-568
Published online September 30, 2018
© 2018 Korean Statistical Society.

Joonsung Kang1,a

aDepartment of Information Statistics, Gangneung-Wonju national University, Korea
Correspondence to: Department of Information Statistics, Gangneung-Wonju National University, Jukheon-gil 7, Gangneung-si 25457, Republic of Korea. E-mail: mkang@gwnu.ac.kr
Received July 17, 2018; Revised August 29, 2018; Accepted August 30, 2018.
 Abstract
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 α and π0 (the proportion of true null); however, the FDR procedure for test statistics based upon normal theory (ANOVA) fails to control FDR.
Keywords : classification, distribution-free test, false discovery rate, M-estimator, union-intersection principle