Universally consistent regression function estimation using hierarchical \(B\)-splines (Q1283852)

Estimation of multivariate regression functions from i.i.d. data is considered. By empirical \(L_2\)-error minimization over data-dependent spaces of polynomial spline functions the estimates have been constructed. For univariate regression function estimation these spaces are spline-spaces with data-dependent knot sequences. In the multivariate case, the author uses so-called hierarchical spline spaces which are defined as a linear span of tensor product \(B\)-splines with nested knot sequences. This paper shows the strong \(L_2\)-consistency of the estimators without any condition on the underlying distribution.