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PATTERN RECOGNITION VIA ROBUST SMOOTHING WITH APPLICATION TO LASER DATA
Author(s) -
Grillenzoni Carlo
Publication year - 2007
Publication title -
australian and new zealand journal of statistics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.434
H-Index - 41
eISSN - 1467-842X
pISSN - 1369-1473
DOI - 10.1111/j.1467-842x.2007.00469.x
Subject(s) - smoothing , classification of discontinuities , mathematics , estimator , nonparametric statistics , kernel (algebra) , bounded function , nonlinear system , nonparametric regression , robust statistics , algorithm , robustness (evolution) , mathematical optimization , jump , statistics , mathematical analysis , biochemistry , physics , chemistry , quantum mechanics , combinatorics , gene
Summary Nowadays airborne laser scanning is used in many territorial studies, providing point data which may contain strong discontinuities. Motivated by the need to interpolate such data and preserve their edges, this paper considers robust nonparametric smoothers. These estimators, when implemented with bounded loss functions, have suitable jump‐preserving properties. Iterative algorithms are developed here, and are equivalent to nonlinear M‐smoothers, but have the advantage of resembling the linear Kernel regression. The selection of their coefficients is carried out by combining cross‐validation and robust‐tuning techniques. Two real case studies and a simulation experiment confirm the validity of the method; in particular, the performance in building recognition is excellent.