**统计与管理学院****2017****年学术报告第****9****期**【主 题】

**Hypothesis testing for quantitative trait locus effects in both mean and variance in genetic backcross studies**【报告人】 刘关福, Ph.D. Candidate

华东师范大学

【时 间】 2017年03月20日（星期一）09:30－10:30

【地 点】 上海财经大学统计与管理学院大楼1208室

【摘 要】Testing the existence of a quantitative trait locus (QTL) effect is an important task in QTL mapping studies. Most studies concentrate on the case where the phenotype distributions of different QTL groups follow normal distributions with the same unknown variance. In practice, the genotype distributions may deviate from normal, and ignoring the potential heterogeneity in the variability may decrease the power of the QTL detection. In this paper we make a more general assumption that the genotype distributions come from a location-scale distribution family, and we study the asymptotic behavior of the likelihood ratio test (LRT) for testing the existence of a QTL effect in genetic backcross studies. We show that the limiting distribution of the LRT for the existence of the QTL effect in both mean and variance is the supremum of a chi-square process when the QTL location is unknown. We further identify an explicit representation for this limiting distribution, which can be used to rapidly determine the critical values of the LRT. As a complement, we study the limiting distribution of the LRT and its explicit representation for the existence of the QTL effect in the mean only. None of the developed asymptotic results relies on the bounded parameter space assumption for the mean parameter, which is commonly assumed in existing studies. Local power analyses are also investigated. Simulation studies are used to evaluate the asymptotic results, and a real-data example is included for illustration.

【邀请人】 冯兴东