## Function Estimation With Locally Adaptive Dynamic Models (1998)

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Venue: | Computational Statistics |

Citations: | 12 - 8 self |

### BibTeX

@ARTICLE{Lang98functionestimation,

author = {Stefan Lang and Eva-Maria Fronk and Ludwig Fahrmeir},

title = {Function Estimation With Locally Adaptive Dynamic Models},

journal = {Computational Statistics},

year = {1998},

volume = {17},

pages = {479--500}

}

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### Abstract

this paper, we present a Bayesian nonparametric approach, which is more closely related to spline fitting with locally adaptive penalties. Abramovich and Steinberg (1996) generalize the common penalized least squares criterion for smoothing splines with a global smoothing parameter by introducing a variable smoothing parameter into the roughness penalty. For estimation, they propose a two-step procedure: First a smoothing spline is fitted with a constant smoothing parameter chosen by generalized cross-validation. Then an estimate for the variable smoothing parameter is constructed, based on the derivatives of this pilot estimate, and is plugged into their locally adaptive penalty to fit the smoothing spline in a second step. Ruppert and Carroll (2000) propose P-splines based on a truncated power series basis and di#erence penalties on the regression coe#cients with locally adaptive smoothing parameters. The latter are obtained by linear interpolation from a smaller number of smoothing parameters, defined for a subset of knots and estimated by generalized cross-validation

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