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Meta-analysis is a statistical method to combine results from multipleclinical or genomic studies with the same or similar research problems. It hasbeen widely use to increase statistical power in finding clinical or genomicdifferences among different groups. One major category of meta-analysis iscombining p-values from independent studies and the Fisher's method is one ofthe most commonly used statistical methods. However, due to heterogeneity ofstudies, particularly in the field of genomic research, with thousands offeatures such as genes to assess, researches often desire to discover thisheterogeneous information when identify differentially expressed genomicfeatures. To address this problem, \citet{Li2011adaptively} proposed veryinteresting statistical method, adaptively weighted (AW) Fisher's method, wherebinary weights, $0$ or $1$, are assigned to the studies for each feature todistinguish potential zero or none-zero effect sizes. \citet{Li2011adaptively}has shown some good properties of AW fisher's method such as the admissibility.In this paper, we further explore some asymptotic properties of AW-Fisher'smethod including consistency of the adaptive weights and the asymptotic Bahaduroptimality of the test.

Properties of adaptively weighted Fisher's method