Curve and surface fitting with splines
Curve and surface fitting with splines
Simultaneous non-parametric regressions of unbalanced longitudinal data
Computational Statistics & Data Analysis
Rank-deficient and discrete ill-posed problems: numerical aspects of linear inversion
Rank-deficient and discrete ill-posed problems: numerical aspects of linear inversion
Estimation in generalized linear models for functional data via penalized likelihood
Journal of Multivariate Analysis
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This paper introduces a new nonparametric estimator based on penalized regression splines for linear operator equations when the data are noisy. A local roughness penalty that relies on local support properties of B-splines is introduced in order to deal with spatial heterogeneity of the function to be estimated. This estimator is shown to be consistent under weak conditions on the asymptotic behaviour of the singular values of the linear operator. Furthermore, in the usual non-parametric settings, it is shown to attain optimal rates of convergence. Then its good performances are confirmed by means of a simulation study.