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Heritability Estimation in High-dimensional Mixed Models : Theory and Applications.

Abstract : We study statistical methods toestimate the heritability of a biological trait,which is the proportion of variations of thistrait that can be explained by genetic factors.First, we propose to study the heritability ofquantitative traits using high-dimensionalsparse linear mixed models. We investigate thetheoretical properties of the maximumlikelihood estimator for the heritability and weshow that it is a consistent estimator and that itsatisfies a central limit theorem with a closedformexpression for the asymptotic variance.This result, supported by an extendednumerical study, shows that the variance of ourestimator is strongly affected by the ratiobetween the number of observations and thesize of the random genetic effects. Moreprecisely, when the number of observations issmall compared to the size of the geneticeffects (which is often the case in geneticstudies), the variance of our estimator is verylarge. This motivated the development of avariable selection method in order to capturethe genetic variants which are involved themost in the phenotypic variations and providemore accurate heritability estimations. Wepropose then a variable selection methodadapted to high dimensional settings and weshow that, depending on the number of geneticvariants actually involved in the phenotypicvariations, called causal variants, it was a goodidea to include or not a variable selection stepbefore estimating heritability.The last part of this thesis is dedicated toheritability estimation for binary data, in orderto study the proportion of genetic factorsinvolved in complex diseases. We propose tostudy the theoretical properties of the methoddeveloped by Golan et al. (2014) for casecontroldata, which is very efficient in practice.Our main result is the proof of the consistencyof their heritability estimator.
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Anna Bonnet. Heritability Estimation in High-dimensional Mixed Models : Theory and Applications.. Statistics [math.ST]. Université Paris-Saclay, 2016. English. ⟨NNT : 2016SACLS498⟩. ⟨tel-01568293⟩

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