Abstract
The advent of complete genetic linkage maps of DNA markers has made the systematic study of mapping quantitative trait loci (QTL) in experimental organisms feasible. In recent years, extensive methodological research on QTL mapping has been performed, Chen and Chen (2005) recently considered the statistical inference problems in the interval mapping method under finite normal mixture models. This article examines the asymptotic null distribution of the likelihood ratio test in finite mixture models with general kernel functions. The limiting null distribution is found to be free of the choice of a kernel function. Technical details are given to the kernel functions with a single parameter under backross populations. Extension to the finite mixture models with presence of a structure parameter is discussed and proposed. The EM algorithm for approximating the MLE's is also discussed.
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