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A certain invariance property of BLUE in a whole‐genome regression context
Author(s) -
Gianola Daniel,
Fernando Rohan L.,
Garrick Dorian J.
Publication year - 2019
Publication title -
journal of animal breeding and genetics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.689
H-Index - 51
eISSN - 1439-0388
pISSN - 0931-2668
DOI - 10.1111/jbg.12378
Subject(s) - covariance , context (archaeology) , estimator , covariance matrix , genome , property (philosophy) , mathematics , random effects model , uncorrelated , linear regression , best linear unbiased prediction , invariant (physics) , biology , genetics , statistics , computational biology , evolutionary biology , computer science , artificial intelligence , medicine , gene , selection (genetic algorithm) , meta analysis , paleontology , philosophy , epistemology , mathematical physics
A curious result from mixed linear models applied to genome‐wide association studies was expanded. In particular, a model in which one or more markers are considered as fixed but are allowed to contribute to the covariance structure by treating such markers as random as well was examined. The best linear unbiased estimator of marker effects is invariant with respect to whether those markers are employed in constructing a genomic relationship matrix or are ignored, provided marker effects are uncorrelated with those not being tested. Also, the implications of regarding some marker effects as fixed when, in fact, these possess a non‐trivial covariance structure with those declared as random were examined.