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In the era of big data, with the rapidly evolving high-throughput technology in genomics, massive amounts of genomic data have been generated to measure a variety of genomic features. Each of these data types has unique characteristics while sharing some commonalities. Some arising issues in these data types pose new challenges to traditional statistical methods in data analyses. , , In this dissertation, I developed tailored statistical methods and extended these methods to more general frameworks for related statistical problems. The methods developed in this work was motivated by three related but distinct areas of genomics research: multi-tissue gene expression and expression-quantitative-trait-loci studies, quantitative proteomics studies, and gene-environment interaction in genetic association studies. The proposed statistical methods accounted for the unique data structures in each data type. In particular, some samples or measurements were naturally or experimentally clustered and may have ignorable or non-ignorable missing values. It has been shown that failing to account for these data characteristics may result in unfaithful conclusions or biased/inefficient estimation. Furthermore, with the goal of detecting individually weak but collectively strong effects of interest, I proposed multivariate analysis methods that jointly analyze multiple functionally related genomic features, as complementary approaches to standard univariate analyses. , , All of the methods developed here are computationally efficient and can be scaled up for high-dimensional data analysis. I developed R packages for each method. I conducted extensive simulation studies to examine the performance of the proposed methods and compared each with existing relevant approaches. I also applied the proposed statistical methods to each of the motivating data sets and obtained new biological results. In the end of each of the three methods chapters, I discussed general applicability of these methods and potential future directions.


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