Asymptotically exact nonparametric hypothesis testing in sup-norm and at a fixed point

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Multiscale testing of qualitative hypotheses (2001, methodology): “Ing ster (1993) or Lepski and Tsybakov (2000) ].”
Sharp Adaptive Estimation of Linear Functionals (2001, background): “Note that if T f = f 0 and 0 ∫ gs 1 1 ∞, the kernel Ks has a particular form Ks = K0s where K0s = gs 1 1 /∫ gs 1 1 This can be shown in a simple way [see, e.g., Lemma 1 of Lepski and Tsybakov (2000)].”
Goodness-of-fit testing and quadratic functional estimation from indirect observations (2006, methodology): “Exact minimax rates have been found; see, for example, Lepski and Tsybakov [22] for the regression model with pointwise and sup-norm distances.”
Simple and honest confidence intervals in nonparametric regression (2016, unknown): “3 Optimal kernel By Low (1995), the bias-sd optimizing kernel takes the form t 7→ f ∗ δ,M(t)/ ∫ X f ∗ δ,M(u) du for some δ, so this implies that k∗(t) = κ∗(t)/ ∫ X κ ∗(u) du is the optimal kernel.”
Asymptotically exact minimax estimation in sup-norm for anisotropic Hölder classes (2004, background): “This is explained in Donoho (1994) and Lepski and Tsybakov (2000).”