Abstract

We derive simple, closed-form estimators of variance components of genetic

interest, including the heritability and variance of environmental errors, in genomewide association studies (GWAS) involving Biobank-size number of individuals. Con-

sistency and asymptotic normality of the proposed estimators are established. Inferential analyses, including confidence intervals and hypothesis testing, for variance

components of genetic interest are developed based on the asymptotic distribution.

The method has significant advantage over the existing BOLT-REML method, designed for such Big GWAS data, in that the latter is not capable of carrying out the

inferential analyses. The new method also has potentially computational advantage.

Finite-sample performance of the proposed method, both in terms of statistical properties of the proposed estimators and confidence intervals and in terms of computa-

tional efficiency, is studied empirically and compared with the BOLT-REML method.

Empirical comparison also shows that our method has significant computational advantage over a moment-matching method called mmhe, and similar statistical per-

formance as mmhe. While most of the theoretical results are established under the

assumption of independent single nucleotide polymorphisms (SNPs), we demonstrate

Jiming Jiang’s ORCID ID: 0000-0001-6364-4717.

how to extend the results to the case of C-dependent SNPs. A real-data example of

the UK Biobank data is discussed.

Key words and phrases: ANOVA, Big GWAS Data, heritability, proportion of causal SNPs, random matrix theory, variance components 1

Information

Preprint No.SS-2025-0022
Manuscript IDSS-2025-0022
Complete AuthorsJiming Jiang, Leqi Xu, Jiangshan Zhang, Hongyu Zhao
Corresponding AuthorsJiming Jiang
Emailsjimjiang@ucdavis.edu

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Acknowledgments

Jiang’s research was partially supported by the NSF grants DMS-1713120

and DMS-1914465. Zhao’s research was partially supported by the NSF grant

DMS-1713120 and NIH grants R01 GM134005 and R01 HG012735.

Supplementary Materials

The Supplementary Material contains proofs of the theoretical results.

Supplementary materials are available for download.