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Optimal Estimation of Genetic Relatedness in High-Dimensional Linear Models

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  • Zijian Guo
  • Wanjie Wang
  • T. Tony Cai
  • Hongzhe Li

Abstract

Estimating the genetic relatedness between two traits based on the genome-wide association data is an important problem in genetics research. In the framework of high-dimensional linear models, we introduce two measures of genetic relatedness and develop optimal estimators for them. One is genetic covariance, which is defined to be the inner product of the two regression vectors, and another is genetic correlation, which is a normalized inner product by their lengths. We propose functional de-biased estimators (FDEs), which consist of an initial estimation step with the plug-in scaled Lasso estimator, and a further bias correction step. We also develop estimators of the quadratic functionals of the regression vectors, which can be used to estimate the heritability of each trait. The estimators are shown to be minimax rate-optimal and can be efficiently implemented. Simulation results show that FDEs provide better estimates of the genetic relatedness than simple plug-in estimates. FDE is also applied to an analysis of a yeast segregant dataset with multiple traits to estimate the genetic relatedness among these traits. Supplementary materials for this article are available online.

Suggested Citation

  • Zijian Guo & Wanjie Wang & T. Tony Cai & Hongzhe Li, 2019. "Optimal Estimation of Genetic Relatedness in High-Dimensional Linear Models," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 114(525), pages 358-369, January.
    • Handle: RePEc:taf:jnlasa:v:114:y:2019:i:525:p:358-369
    DOI: 10.1080/01621459.2017.1407774
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    Cited by:

    1. The Tien Mai, 2023. "Reliable Genetic Correlation Estimation via Multiple Sample Splitting and Smoothing," Mathematics, MDPI, vol. 11(9), pages 1-13, May.
    2. Xingyu Chen & Lin Liu & Rajarshi Mukherjee, 2024. "Method-of-Moments Inference for GLMs and Doubly Robust Functionals under Proportional Asymptotics," Papers 2408.06103, arXiv.org.
    3. Qingliang Fan & Zijian Guo & Ziwei Mei, 2022. "A Heteroskedasticity-Robust Overidentifying Restriction Test with High-Dimensional Covariates," Papers 2205.00171, arXiv.org, revised May 2024.
    4. Adel Javanmard & Jason D. Lee, 2020. "A flexible framework for hypothesis testing in high dimensions," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 82(3), pages 685-718, July.

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