Some Statistical Aspects Of The Complex Interval Mapping For QTL Detection

Quantitative trait loci (QTLs) mapping is the procedure for finding and locating QTLs, which is of importance in medical research, plant and animal breeding. Conventional methods including single marker analysis and interval mapping are based on the single locus model. Unfortunately, a large portion of quantitative traits are affected by more than one genes. To increase the accuracy, composite interval mapping was proposed by Zeng (1994). However, some related statistical problems for composite interval mapping remain unsolved. The purpose of this thesis is to study these problems. We only present the results for the backcross population. Note that they can be extended to the intercross population.Due to the mixture model, composite interval model is irregular in sense of the identifi-ablity. Therefore, in this thesis, we first define a new parameter system and investigate the identifiablity of the distribution family through the new parameterization. Then, we establish the consistency of the MLEs of the new parameters. Moreover, based on this property, we obtain the consistency of the MLEs for the putative QTLs effects and locations. After solving the problem about the identifiablity of the distribution family, our future research will derive the asymptotic null distribution of the likelihood ratio test (LRT) statistic for composite interval mapping.