Abstract:
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Motivated by the analysis of RNA sequencing (RNA-seq) data for genes differentially expressed across multiple conditions, we consider detecting rare and faint linear combinations of the regression coefficients (which we call signals) in high-dimensional response variables which are usually count data. More generally, we address the signal detection problem under generalized linear models. We propose a test statistic that carries out a multi-level thresholding on maximum likelihood estimators (MLEs) of the signals, which allows removal of the dimensions with no signals. A Cramer type moderate deviation result for multi-dimensional MLEs is derived, which is needed to obtain the asymptotic distribution of the thresholding test statistic. Extensions to generalized linear mixed models are made, where Gauss-Hermite quadrature is used to approximate the MLEs of such models. Numerical simulations and a case study on maize RNA-seq data are conducted to confirm and demonstrate the proposed testing approaches.
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