Anisotropic smoothing splines in problems with factorial design of experiments (Q492752)

The author addresses the problem of finding an estimate of a function \(f_0\) of many variables from a given data sample \(\{x_i \in \Omega, \,_i = f_0(x_i) + \xi_i\}\), where \(\Omega \subset [0, 1]^d\) is a domain in \(\mathbb {R}^d\) and \(\xi_i\) is white noise. The function \(f_0\) is assumed to belong to a suitable Sobolev space. The estimate is constructed by using a tensor product of \(B\)-splines. The author defines an algorithm for finding such an estimate, and discusses several properties, including the computational cost of the algorithm and an upper bound for the error.