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Problems involving the simultaneous estimation of multiple parameters arise in many areas of theoretical and applied statistics. A canonical example is the estimation of a vector of normal means. Frequently, structural information about relationships between the parameters of interest is available. For example, in a gene expression denoising problem, genes with similar functions may have similar expression levels. Despite its importance, structural information has not been well-studied in the simultaneous estimation literature, perhaps in part because it poses challenges to the usual geometric or empirical Bayes shrinkage estimation paradigms. This article proposes that some of these challenges can be resolved by adopting an alternate paradigm, based on regression modeling. This approach can naturally incorporate structural information and also motivates new shrinkage estimation and inference procedures. As an illustration, this regression paradigm is used to develop a class of estimators with asymptotic risk optimality properties that perform well in simulations and in denoising gene expression data from a single cell RNA-sequencing experiment. [ABSTRACT FROM AUTHOR]

Genome-wide association studies (GWAS) and differential expression analyses have had limited success in finding genes that cause complex diseases such as heart failure (HF), a leading cause of death in the United States. This article proposes a new statistical approach that integrates GWAS and expression quantitative trait loci (eQTL) data to identify important HF genes. For such genes, genetic variations that perturb its expression are also likely to influence disease risk. The proposed method thus tests for the presence of simultaneous signals: SNPs that are associated with the gene’s expression as well as with disease. An analytic expression for thep-value is obtained, and the method is shown to be asymptotically adaptively optimal under certain conditions. It also allows the GWAS and eQTL data to be collected from different groups of subjects, enabling investigators to integrate public resources with their own data. Simulation experiments show that it can be more powerful than standard approaches and also robust to linkage disequilibrium between variants. The method is applied to an extensive analysis of HF genomics and identifies several genes with biological evidence for being functionally relevant in the etiology of HF. It is implemented in the R packagessa. Supplementary materials for this article are available online. [ABSTRACT FROM PUBLISHER]