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Title: The SgenoLasso for gene mapping and genomic prediction Authors:  Celine Delmas - INRAE (France)
Charles-Elie Rabier - Montpellier University (France) [presenting]
Abstract: The focus is on the problem of detecting Quantitative Trait Loci, so-called QTL (genes influencing a quantitative trait which can be measured) on a given chromosome $[0,T]$. We assume a linear model on the quantitative trait $Y_i=\mu+\sum_{s=1}^mX_i(t_s^{\star})q_s+\sigma \epsilon_i$ where $\mu$ is the global mean, $X_i(\cdot)$ the genome information, $\epsilon_i$ a Gaussian white noise, $\sigma^2$ the environmental variance, $m$ the number of QTL, $q_s$ and $t_s^{\star}$ denote respectively the QTL effect and the location of the $s$th QTL. The quantitative trait $Y_i$ is measured on all the individuals $i$ whereas the genome information $X_i$ is available only on extreme individuals and only at fixed locations. First, we derive theoretical properties of the score test process and likelihood ratio test process along the chromosome under the null hypothesis of no QTL on $[0,T]$ and under the alternative hypothesis that there exits $m$ QTL on the chromosome. We deduce a new method, called SgenoLasso, to estimate the number of QTL, their locations, and their effects. This method will also be used for genomic prediction. It will be compared to classical methods (Lasso, Group Lasso, Elastic Net, RaLasso, Bayesian Lasso) on simulated data and applied to real data.