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Design of kernel M-smoothers for spatial data. (English) Zbl 1248.62047

Summary: Robust nonparametric smoothers have been proved effective to preserve edges in image denoising. As an extension, they should be capable to estimate multivariate surfaces containing discontinuities on the basis of a random spatial sampling. A crucial problem is the design of their coefficients, in particular those of the kernels which concern robustness. In this paper it is shown that bandwidths which regard smoothness can consistently be estimated, whereas those which concern robustness cannot be estimated with plug-in and cross-validation criteria. Heuristic and graphical methods are proposed for their selection and their efficacy is proved in simulation experiments.

MSC:

62G05 Nonparametric estimation
62G35 Nonparametric robustness
62H12 Estimation in multivariate analysis
62H11 Directional data; spatial statistics
65C60 Computational problems in statistics (MSC2010)
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