Nonparametric methods for big and complex datasets under a reproducing kernel Hilbert space framework
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Large and complex data have been generated routinely from various sources, for instance, time course biological studies and social media. Classic nonparametric models, such as smoothing spline ANOVA models, are not well equipped to analyze such large and complex data. To overcome these challenges, I propose novel nonparametric methods under a reproducing kernel Hilbert space framework to (1) significantly reduce daunting computational costs of selecting smoothing parameters for smoothing spline ANOVA models; (2) model the data with a functional response and a functional predictor; (3) accurately identify differentially expressed genes in time course RNA-seq data. To validate my proposed methods, I conduct simulation studies and apply the proposed methods to real data studies. In the end, I present derivations and theoretical proofs.