| Various statistical approaches have been developed to identify QTLs by using molecular markers, but most are parametrically based. The normality assumption of the underlying distribution, greatly simplifies the testing and estimation problems. However, if this assumption is violated, false detection of a major locus may occur. In this dissertation, we focus on developing some efficient and robust methodologies for finite mixture problems, which can then be applied to QTL analysis.;First, we propose a semiparametric alternative which assumes that the log ratio of the component densities satisfies a linear model, with the baseline density unspecified. The partial likelihood proposed is shown to give consistent and asymptotically normal estimators. The asymptotic null distribution of the log-partial likelihood ratio is chi-square.;We then develop a nonparametric method by extending Wilcoxon-rank based tests to estimation problems. Simulation results show that the linear rank based estimator is unbiased and more efficient than the parametric estimator when data are non-normal.;Further, in this dissertation, we consider some practical statistical issues in QTL analysis where several crosses originate in multiple inbred parents. Our results show that ignoring background genetic variation in different crosses may lead to biased estimates of QTL effects and loss of efficiency. Threshold and power approximations are derived by extending earlier results based on the Ornstein-Uhlenbeck diffusion process. Several common designs are evaluated in terms of their power to detect QTLs. |
