Pointwise and sup-norm sharp adaptive estimation of functions on the Sobolev classes

摘要: The problem of nonparametric function estimation in the Gaussian white noise model is considered. It assumed that unknown function belongs to one Sobolev classes, with an regularity parameter. Asymptotically exact adaptive estimators functions are proposed on scale respect pointwise and sup-norm risks. shown that, unlike case $L_2$-risk, a loss efficiency under adaptation is inevitable here. Bounds value are obtained.