Uniform reconstruction of Gaussian processes

[摘要] We consider a Gaussian process X with smoothness comparable to the Brownian motion. We analyze reconstructions of X which are based on observations at finitely many points. For each realization of X the error is defined in a weighted supremum norm, the overall error of a reconstruction is defined as the pth moment of this norm. We determine the rate of the minimal errors and provide different reconstruction methods which perform asymptotically optimal. In particular, we show that linear interpolation at the quantiles of a certain density is asymptotically optimal. (C) 1997 Elsevier Science B.V.

[发布日期] 1997-07-31

[关键词] Brownian motion;Sacks-Ylvisaker conditions;asymptotically optimal designs;reproducing kernel Hilbert space;regular sequence;uniform norm