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Tuning-free penalized maximum likelihood to improve estimates of genetic covariance matrices

Partitioning of the phenotypic variation into its causal components to determine genetic 2 parameters is one of the basic tasks in quantitative genetics. For multiple characteristics of 3 interest, this involves the estimation of covariance matrices due to genetic and other effects. 4 It is well known that such estimates can be subject to substantial sampling variation, as the 5 number of parameters to be estimated generally increases quadratically with the number of 6 traits considered. In particular, it has been recognized early on that the eigenvalues of sample 7 covariance matrices are systematically biased – with the largest eigenvalues overestimated 8 and the smallest values underestimated – and that a major proportion of the sampling 9 variation of covariance matrices can be attributed to this over-dispersion (Lawley, 1956; 10 Ledoit & Wolf, 2004). 11