"Treelet Covariance Smoothers"

Next generation sequencing technology is enabling researchers to establish the genetic basis of complex traits and diseases.Genome-Wide Association Studies (GWAS) have made incredible progress in the last decade identifying genes that increase predisposition to disease, tracing genetic mutation, and analyzing the role genetic variation plays in gene expression. These discoveries have come, in part, due to the arsenal of statistical techniques which extract meaningful information from genetic data. A considerable amount of the success in most studies relies on the accurate estimation of familial relatedness. Recently, this problem has been formulated as accurately estimating sparse variance-covariance matrices. By utilizing a Treelet decomposition, we design two methods, Treelet Covariance Blocking (TCB) and Treelet Covariance Blocked Smoothing (TCBS), which exploit familial clusters inherent in large population-based samples. We show through extensive simulation studies that these methods refine the estimation of distant relatedness. Finally, we demonstrate the effectiveness of these methods by applying them to the estimation of narrow-sense heritability of two polygenic phenotypes in the Health Aging and Body Composition (ABC) study.