Some Aspects of the Spline Smoothing Approach to Non-Parametric Regression Curve Fitting

Journal of the Royal Statistical Society: Series B (Statistical Methodology) · 1985 · Volume 47 · Issue 1

DOI: 10.1111/j.2517-6161.1985.tb01327.x

Abstract

Non-parametric regression using cubic splines is an attractive, flexible and widely-applicable approach to curve estimation. Although the basic idea was formulated many years ago, the method is not as widely known or adopted as perhaps it should be. The topics and examples discussed in this paper are intended to promote the understanding and extend the practicability of the spline smoothing methodology. Particular subjects covered include the basic principles of the method; the relation with moving average and other smoothing methods; the automatic choice of the amount of smoothing; and the use of residuals for diagnostic checking and model adaptation. The question of providing inference regions for curves – and for relevant properties of curves – is approached via a finite-dimensional Bayesian formulation.

Keywords

roughness penalty, smoothing, weight function, variable kernel, cross-validation, automatic smoothing, residuals, regression diagnostics, local reweighting, change point, model choice, bayesian inference, empirical bayes, b-splines, growth curves, functionals of curves, robust smoothing, generalized smoothing, surface estimation

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