Spline smoothing over difficult regions


Address for correspondence : Tim Ramsay, McLaughlin Centre for Population Health Risk Assessment, University of Ottawa, Room 321, 1 Stewart Street, Ottawa, K1N 6N5, Canada.
E-mail: tramsay@uottawa.ca


Summary. It is occasionally necessary to smooth data over domains in 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.