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Error estimates for multivariate regression on discretized function spaces

: Bohn, B.; Griebel, M.

Volltext ()

SIAM journal on numerical analysis 55 (2017), Nr.4, S.1843-1866
ISSN: 0036-1429
Deutsche Forschungsgemeinschaft DFG
SFB 1060 ""The Mathematics of Emergent Effects"
Zeitschriftenaufsatz, Elektronische Publikation
Fraunhofer SCAI ()

In this paper, we will discuss the discretization error for the regression setting and derive error bounds relying on the approximation properties of the discretized space. Furthermore, we will point out how the sampling error and the discretization error interact and how they can be balanced appropriately. We will present two examples based on tensor product spaces (sparse grids, hyperbolic crosses) which provide a suitable approach in the case of large sample sets in moderate dimensions.