Seminars: Dept Seminar
Testing a Union-of-Cones Null Hypothesis for the Identification of Heterosis
||Friday, July 13
||8:00 am -- 9:00 am
|| Heng Wang
High-parent or low-parent heterosis is a genetic phenomenon that occurs when the mean trait value of offspring is more extreme than that of either parent. We discuss statistical tests that can be used to detect heterosis of this type. The null hypothesis of no high-parent or low-parent heterosis constrains a vector of mean parameters to a union of two closed convex cones. This unusual null parameter space leads to a nonstandard testing problem for which we derive both the likelihood ratio test and the intersection-union test. Although these tests are often equivalent, we show that the likelihood ratio test is preferred over the intersection-union test in this case. However, we also show that it is possible to develop a test uniformly more powerful than the
likelihood ratio test. Although such tests are of theoretical interest, we ultimately recommend the likelihood ratio test for use in practical applications.