Improving Kernel-Based Nonasymptotic Simultaneous Confidence Bands
Balázs Csanád Csáji Bálint Horváth
The paper studies the problem of constructing nonparametric simultaneous
confidence bands with nonasymptotic and distribition-free guarantees. The
target function is assumed to be band-limited and the approach is based on the
theory of Paley-Wiener reproducing kernel Hilbert spaces. The starting point of
the paper is a recently developed algorithm to which we propose three types of
improvements. First, we relax the assumptions on the noises by replacing the
symmetricity assumption with a weaker distributional invariance principle.
Then, we propose a more efficient way to estimate the norm of the target
function, and finally we enhance the construction of the confidence bands by
tightening the constraints of the underlying convex optimization problems. The
refinements are also illustrated through numerical experiments.