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Surface and function approximation with nonparametric regression

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Summary

Several methods are considered for the reconstruction of smooth functions and surfaces from noisy measurements. These methods are statistically motivated and belong to the area of nonparametric regression. They include the kernel method, local orthonormal polynomial expansions with prebinning, and locally weighted least squares. The close connections which exists between these methods are pointed out, and equivalent kernels for locally weighted least squares estimates are derived. An application to surface approximation for Iranian soil clay thickness data is discussed. We also consider the case of surfaces with discontinuities. This includes the edge estimation problem, maximum and cube splitting methods for edge estimation and associated two-step procedures for the recovery of the entire surface.

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Authors and Affiliations

  1. University of California, Davis, USA

    Hans-Georg Müller

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  1. Hans-Georg Müller
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Müller, HG. Surface and function approximation with nonparametric regression. Seminario Mat. e. Fis. di Milano 63, 171–211 (1993). https://doi.org/10.1007/BF02925100

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