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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

Citations:

Zbl 0165.21505
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