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Spline smoothing over difficult regions
Author(s) -
Ramsay Tim
Publication year - 2002
Publication title -
journal of the royal statistical society: series b (statistical methodology)
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 6.523
H-Index - 137
eISSN - 1467-9868
pISSN - 1369-7412
DOI - 10.1111/1467-9868.00339
Subject(s) - smoothing , thin plate spline , smoothing spline , spline (mechanical) , mathematics , smoothness , polyharmonic spline , bivariate analysis , euclidean geometry , mathematical optimization , mathematical analysis , spline interpolation , geometry , statistics , engineering , structural engineering , bilinear interpolation
Summary. It is occasionally necessary to smooth data over domains in ℝ 2 with complex irregular boundaries or interior holes. Traditional methods of smoothing which rely on the Euclidean metric or which measure smoothness over the entire real plane may then be inappropriate. This paper introduces a bivariate spline smoothing function defined as the minimizer of a penalized sum‐of‐squares functional. The roughness penalty is based on a partial differential operator and is integrated only over the problem domain by using finite element analysis. The method is motivated by and applied to two sample smoothing problems and is compared with the thin plate spline.