Kernel-Based Interval Estimates of Inverse Dose Response With Applications to Genetic Clines

We investigate nonparametric regression techniques to estimate the distribution of the LD_100α, 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 LD_100α 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.