On interpolations in QTL detection

Céline Delmas (1) , Charles-Elie Rabier (1, 2)

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 (a QTL denotes a quantitative trait locus, i.e. a gene with quantitative effect on a trait) on the interval [0,T] representing a chromosome. Recently, Azais et al. proved that the LRT process was the square of a non linear interpolated process. However, in their study of the same problem, Chang et al. introduced another interpolation. So, why do Azais and Chang find different interpolations ? We correct errors present in the interpolation of Chang and establish the link between the two interpolations. We finally generalize the interpolation of Chang to the alternative hypothesis of a QTL located at t* inside [0,T].

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

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

Céline Delmas, Charles-Elie Rabier. On interpolations in QTL detection. 2012. ⟨hal-00658592⟩