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Free-knot spline smoothing for functional data

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The paper introduces free-knot regression spline estimators for the mean and the variance components of a sample of curves. The asymptotic distribution of the mean estimator is derived, and asymptotic confidence bands are constructed. A comparative simulation study shows that free-knot splines estimate salient features of the functions (such as sharp peaks) more accurately than smoothing splines. This adaptive behaviour is also illustrated by an analysis of weather data.
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Keywords: Functional data analysis; Karhunen–Loève decomposition; Longitudinal data analysis; Variance components

Document Type: Research Article

Affiliations: University of Wisconsin—Milwaukee, USA

Publication date: 2006-09-01

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