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Abstract:
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Testing multiple hypotheses by adapting to auxiliary covariates has gained major attention in recent years, as researchers have increasingly recognized the importance of leveraging contextual information beyond what is offered by the main statistics to devise more powerful procedures for controlling the false discovery rate (FDR). Currently, most cutting-edge covariate-adaptive procedures are developed with the p-values as their main statistics. This, however, warrants a loss of information for the most common two-sided hypotheses, since two-sided p-values are formed from non-bijective transformations of the original test statistics that are generally known as the z-values, such as Wald statistics or t-statistics. In this paper we introduce a z-value based covariate-adaptive (ZAP) approach to multiple testing, which builds upon recent advances in the area but operates on the intact information carried jointly by the z-values and covariates. Our two variant methods of ZAP respectively provide asymptotic and finite-sample FDR controls, with each having its own merits, and both achieve state-of-the-art power performances without relying on strong modeling assumptions.
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