Kernel-Based Interval Estimates of Inverse Dose Response With Applications to Genetic Clines
Degree awarded: Ph.D. Mathematics and Statistics. American University We investigate nonparametric regression techniques to estimate the distribution of the LD100α, 0 <α < 1, the lethal dose where 100α% of subjects show a response. Kernel methods are used to estimate the resulting response probability curve using real and simulated data. We apply and extend these kernel-based estimation procedures to a problem in evolutionary genetics where the prevalence of a genetic trait is mapped. In this setting, distance serves as a dose and the response probability curve is called a cline. We investigate the distributional properties of kernel estimates of LD100α with special attention to the LD20, LD80, and the distance between them, called the cline width. Confidence intervals are constructed for LD20, LD80, and the cline width and small sample properties are investigated through series expansion and simulation.