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Statistics dissertation titled "Identification of Differentially Expressed Genes via Knockoff Statistics in Single-cell RNA Sequencing Data Analysis". The knockoff filter is a recently introduced framework for multiple testing with guaranteed false discovery rate (FDR) control and it is particularly powerful for high-dimensional conditional inference. The method relies on accurately estimating the distribution of the explanatory variables. The work proposes knockoff constructions based on a latent factor model to recover the missing data, and to construct knockoff variables more computationally efficiently, which is crucial under high-dimensional settings. With concerns about the randomness of knockoffs in mind, we also introduce recent advancements in derandomization---multiple knockoffs and the e-BH procedure. Extensive simulations demonstrate that the proposed methods control the FDR, and have a higher power than the original knockoff constructions by Candés et al.. Furthermore, we show that the knockoff filter is robust against unaddressed potential confounders. We also applied the methods on differentially expressed gene (DEG) analysis with single-cell RNA sequencing data and the discovered genes are cross-referenced with DEGs from other studies, confirming that some of the reported DEGs are mutually shared, without requiring log fold change screening.

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