On nonparametric tests of positivity/monotonicity/convexity
Speaker: Kenta Takatsu
Abstract: I will share a classical result on the minimax rate for testing qualitative hypotheses associated with a nonparametric regression function: if the function satisfies certain shape constraints such as monotonicity. The proposed test involves the estimation of the Lr distance between the regression function and the convex cone. The main technical focus will be on the derivation of lower bound, which resembles the classical method for nonsmooth functionals by Lepski et al. Although this is a spiritual follow-up to Tudor’s talk on nonsmooth functionals, the attendance to his talk is not required.