Abstract:
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Random-effects models are one of the most widely studied and important classes of models in applied statistics. Genetics is one classical application area for random-effects models, where they have been used since at least the 1950s. More recently, spurred on by technological breakthroughs and the accompanying widespread availability of vast genomic datasets, researchers in genetics have been using random-effects models in creative new ways, in applications ranging from estimating heritability to the analysis of microarray data. These new applications of random-effects models have (i) shed light on important scientific questions, (ii) raised interesting and challenging questions about their statistical validity, and (iii) brought new computational issues to the forefront. In this talk, we will discuss new technical results that we have derived, which may lay the foundation for understanding the theoretical validity of these (and other) novel applications of random-effects models. Our theoretical results are primarily related to quadratic forms in statistics. We will also discuss computational approaches for these problems.
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