Figure 4:

Single realizations of the output of our method at confidence level 90% for the three noise fields (rows) and for sample sizes n = 40,60,80 (columns) with the target function μ(s) from Figure 3a. In all pictures we show a heat map of the estimator ${\widehat{\mu }}_n(s)$, the boundary of A_c(μ) (solid purple) and $A_c(\widehat{\mu })$ (dashed purple) and the boundaries of ${\widehat{A}}_c^{+}$ (red) and ${\widehat{A}}_c^{-}$ (green). The threshold a was obtained using the multiplier bootstrap and the plug-in estimate of the boundary A_c.