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Public genomic repositories are notoriously lacking in racially and ethnically diverse samples. This limits the reaches of exploration and has in fact been one of the driving factors for the initiation of the All of Us project. Our particular focus here is to provide a model-based framework for accurately predicting DNA methylation from genetic data using racially sparse public repository data. Epigenetic alterations are of great interest in cancer research but public repository data is limited in the information it provides. However, genetic data is more plentiful. Our phenotype of interest is cervical cancer in The Cancer Genome Atlas (TCGA) repository. Being able to generate such predictions would nicely complement other work that has generated gene-level predictions of gene expression for normal samples. We develop a new prediction approach which uses shared random effects from a nested error mixed effects regression model. The sharing of random effects allows borrowing of strength across racial groups greatly improving predictive accuracy. Additionally, we show how to further borrow strength by combining data from different cancers in TCGA even though the focus of our predictions is DNA methylation in cervical cancer. We compare our methodology against other popular approaches including the elastic net shrinkage estimator and random forest prediction. Results are very encouraging with the shared classified random effects approach uniformly producing more accurate predictions – overall and for each racial group. 

A small area typically refers to a subpopulation or domain of interest for which a reliable direct estimate, based only on the domain-specific sample, cannot be produced due to small sample size in the domain. While traditional small area methods and models are widely used nowadays, there have also been much work and interest in robust statistical inference for small area estimation (SAE). We survey this work and provide a comprehensive review here.We begin with a brief review of the traditional SAE methods. We then discuss SAEmethods that are developed under weaker assumptions and SAE methods that are robust in certain ways, such as in terms of outliers or model failure. Our discussion also includes topics such as nonparametric SAE methods, Bayesian approaches, model selection and diagnostics, and missing data. A brief review of software packages available for implementing robust SAE methods is also given.