ABSTRACT
In this talk we discuss two-stage adaptive designs based on nonparametric procedures for estimating an inverse regression function at a given point. Specifically, isotonic regression is used at stage one to obtain an initial estimate and (smoothed) isotonic regression in the vicinity of this estimate at stage two. It is shown that such two stage plans accelerate the convergence rate of one-stage procedures and under suitable choices of the parameters involved can achieve the parametric n^{1/2} rate. Both Wald and Likelihood Ratio type confidence intervals for the threshold value of interest are investigated and the latter type are recommended in applications due to their simplicity and robustness. The developed plans are illustrated through a comprehensive simulation study and an application to car fuel efficiency data.