Abstract: The advent of complete genetic linkage maps of DNA markers has made the systematic study of mapping the quantitative trait loci (QTL) in experimental organisms feasible. In recent years, methodological research on QTL mapping has been extensively carried out. However, some related statistical problems remain unsolved. In this article, we consider these problems for the method of interval mapping proposed by Lander and Botstein (1989). We tackle the intrinsic non-identifiability of the involved irregular statistical models and establish the consistency of the maximum likelihood estimates of the putative QTL effect and position. We derive by a non-standard approach the asymptotic distribution of the likelihood ratio test (LRT) statistic for QTL detection. Our result provides a structure for the asymptotic distribution which enjoys the invariance property of regular models. The applications of the results to the determination of threshold values or-values of interval mapping for QTL detection are discussed and developed. Simulation studies are performed to compare the new approach with the existing methods. The results are presented only for the backcross model but can be extended easily to the intercross model.
Key words and phrases: Asymptotic distribution, backcross, Gaussian process, identifiability, likelihood ratio test; mixture model, QTL mapping.