In this talk, I will discuss threshold estimation for a regression function in some different settings. The threshold can either be a change–point, i.e. a point of jump discontinuity in an otherwise smooth curve, or the first time that a regression function crosses a certain level. Both problems have numerous applications in a variety of spheres, like biology (pharmacology, dose-response experiments) and engineering. Our goal is to estimate thresholds of this type given a fixed budget of points to sample from, but with the flexibility that batch sampling can be done in several stages, so that adaptive strategies are possible. Our strategy is to use multistage zoom-in procedures to estimate the threshold: an initial fraction of the sample is invested top come up with a first guess, an adequate neighborhood of the first guess is chosen, more points are sampled from this neighborhood and the initial estimate id updated. The procedure continues thus, ending in a finite number of stages. Such zoom-in procedures result in accelerated convergence rates over any one–stage method. Approximations to relative efficiencies are computed and optimal allocation strategies, as well as recipes for construction of confidence sets discussed.

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Last updated: 24 Mar 2023