Multivariate integration and approximation for random fields satisfying Sacks-Ylvisaker conditions. (English) Zbl 0872.62063

Ritter, Klaus; Wasilkowski, Grzegorz W.; Woźniakowski, Henryk

Ann. Appl. Probab. 5, No. 2, 518-540 (1995).

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

Keywords:

L2 approximation; optimal linear estimators; reproducing kernel Hilbert spaces; sharp bounds; minimal errors of linear estimators; multivariate integration; random field; Sacks-Ylvisaker regularity conditions

Citations:

Zbl 0165.21505