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Activity Number: 612 - New Challenges in High-Dimensional Statistical Inference
Type: Topic Contributed
Date/Time: Thursday, August 3, 2017 : 8:30 AM to 10:20 AM
Sponsor: IMS
Abstract #323184
Title: Optimal Estimation of Co-Heritability in High-Dimensional Linear Models
Author(s): Zijian Guo* and Wangjie Wang and Tony Cai and Hongzhe Li
Companies: University of Pennsylvania, Wharton School and National University of Singapore and University of Pennsylvania and University of Pennsylvania
Keywords: Genetic correlations ; genome-wide association studies ; inner product ; minimax rate of convergence ; quadratic functional
Abstract:

Co-heritability is an important concept that characterizes the genetic associations within a pair of quantitative traits. There has been significant recent interest in estimating the co-heritability based on data from the genome-wide association studies (GWAS). This paper introduces two measures of co-heritability in the high-dimensional linear model framework, including the inner product of the two regression vectors and a normalized inner product by their lengths, which can be interpreted as genetic covariance and genetic correlation due to GWAS genetic variants. Functional de-biased estimators (FDEs) are developed to estimate these two co-heritability measures. In addition, estimators of quadratic functionals of the regression vectors are proposed. Both theoretical and numerical properties of the estimators are investigated. In particular, minimax rates of convergence are established and the proposed estimators of the inner product, the quadratic functionals and the normalized inner product are shown to be rate-optimal. Simulation results show that the FDEs significantly outperform the naive plug-in estimates. The FDEs are also applied to analyze a yeast data.


Authors who are presenting talks have a * after their name.

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