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Free‐knot spline smoothing for functional data

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  • Daniel Gervini

Abstract

Summary. 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.

Suggested Citation

  • Daniel Gervini, 2006. "Free‐knot spline smoothing for functional data," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 68(4), pages 671-687, September.
    • Handle: RePEc:bla:jorssb:v:68:y:2006:i:4:p:671-687
    DOI: 10.1111/j.1467-9868.2006.00561.x
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    Cited by:

    1. Laura M. Sangalli & Piercesare Secchi & Simone Vantini & Alessandro Veneziani, 2009. "Efficient estimation of three‐dimensional curves and their derivatives by free‐knot regression splines, applied to the analysis of inner carotid artery centrelines," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 58(3), pages 285-306, July.
    2. van der Linde, Angelika, 2008. "Variational Bayesian functional PCA," Computational Statistics & Data Analysis, Elsevier, vol. 53(2), pages 517-533, December.
    3. Bali, Juan Lucas & Boente, Graciela, 2014. "Consistency of a numerical approximation to the first principal component projection pursuit estimator," Statistics & Probability Letters, Elsevier, vol. 94(C), pages 181-191.
    4. Binder, Harald & Sauerbrei, Willi, 2008. "Increasing the usefulness of additive spline models by knot removal," Computational Statistics & Data Analysis, Elsevier, vol. 52(12), pages 5305-5318, August.
    5. Lakshman S. Thakur & Mikhail A. Bragin, 2021. "Data Interpolation by Near-Optimal Splines with Free Knots Using Linear Programming," Mathematics, MDPI, vol. 9(10), pages 1-12, May.
    6. Gerda Claeskens & Bernard W. Silverman & Leen Slaets, 2010. "A multiresolution approach to time warping achieved by a Bayesian prior–posterior transfer fitting strategy," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 72(5), pages 673-694, November.

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