Multivariate integration and approximation for random fields satisfying Sacks-Ylvisaker conditions. (English) Zbl 0872.62063
Summary: We present sharp bounds on the minimal errors of linear estimators for multivariate integration and \(L_2\)- approximation. This is done for a random field whose covariance kernel is a tensor product of one-dimensional kernels that satisfy the Sacks-Ylvisaker regularity conditions [see J. Sacks and D. Ylvisaker, Ann. math. Stat. 39, 49-69 (1968; Zbl 0165.21505)].
MSC:
62H12 | Estimation in multivariate analysis |
41A55 | Approximate quadratures |
41A50 | Best approximation, Chebyshev systems |
41A63 | Multidimensional problems |
62G05 | Nonparametric estimation |
62M40 | Random fields; image analysis |