Likelihood Ratio Test process for Quantitative Trait Loci detection.

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