Abstract: We study the high-dimensional asymptotic behavior of inferences based on summary statistics that are widely used in genome-wide association studies (GWAS) under model misspecification. The high dimensionality is in the sense that the number of single-nucleotide polymorphisms (SNPs) under consideration may be much larger than the sample size. The model misspecification is in the sense that the number of causal SNPs may be much smaller than the total number of SNPs under consideration. Specifically, we establish two parameters of genetic interest, namely, the consistency and asymptotic normality of the estimators of the heritability and genetic covariance. Our theoretical results are supported by the findings of empirical studies involving simulated and real data.

Key words and phrases: Asymptotic normality, Bernoulli, consistency, genetic covariance, heritability, martingale, model misspecification, random matrix theory.