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Article Dans Une Revue Sankhya: The Indian Journal of Statistics Année : 2007

Estimation of piecewise-smooth functions by amalgamated bridge regression splines

Résumé

We consider nonparametric estimation of a one-dimensional piecewise-smooth function observed with white Gaussian noise on an interval. We propose a two-step estimation procedure, where one first detects jump points by a wavelet-based procedure and then estimates the function on each smooth segment separately by bridge regression splines. We prove the asymptotic optimality (in the minimax sense) of the resulting amalgamated bridge regression spline estimator and demonstrate its efficiency on simulated and real data examples.
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Dates et versions

hal-00394102 , version 1 (10-06-2009)

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  • HAL Id : hal-00394102 , version 1

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Felix Abramovich, Anestis Antoniadis, Marianna Pensky. Estimation of piecewise-smooth functions by amalgamated bridge regression splines. Sankhya: The Indian Journal of Statistics, 2007, 69 (1), pp.1-27. ⟨hal-00394102⟩
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