Likelihood Ratio Test process for Quantitative Trait Loci detection.

Charles-Elie Rabier (1, 2) , Jean-Marc Azaïs (2) , Céline Delmas (1)

1 SAGA - Station d'Amélioration Génétique des Animaux
2 LSP - Laboratoire de Statistique et Probabilités

We consider the likelihood ratio test (LRT) process related to the test of the absence of QTL on the interval [0,T] representing a chromosome (a QTL denotes a quantitative trait locus, i.e. a gene with quantitative effect on a trait). We give the asymptotic distribution of this LRT process under the null hypothesis that there is no QTL on [0,T] and under the general alternative that there exist m QTL on [0,T]. We propose to estimate the number of QTL, their positions and their effects by penalized likelihood. Our results are extended to the case where individuals are structured into families.

Mots clés: chi-square process; Gaussian process; Likelihood Ratio Test; Mixture models; Nuisance parameters present only under the alternative; QTL detection; chi-square process.

Domaines: Théorie [stat.TH]; Statistiques [math.ST]

Charles-Elie Rabier, Jean-Marc Azaïs, Céline Delmas. Likelihood Ratio Test process for Quantitative Trait Loci detection.. 2009. ⟨hal-00421215⟩