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February 1997 Locally adaptive regression splines
Enno Mammen, Sara van de Geer
Ann. Statist. 25(1): 387-413 (February 1997). DOI: 10.1214/aos/1034276635


Least squares penalized regression estimates with total variation penalties are considered. It is shown that these estimators are least squares splines with locally data adaptive placed knot points. The definition of these variable knot splines as minimizers of global functionals can be used to study their asymptotic properties. In particular, these results imply that the estimates adapt well to spatially inhomogeneous smoothness. We show rates of convergence in bounded variation function classes and discuss pointwise limiting distributions. An iterative algorithm based on stepwise addition and deletion of knot points is proposed and its consistency proved.


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Enno Mammen. Sara van de Geer. "Locally adaptive regression splines." Ann. Statist. 25 (1) 387 - 413, February 1997.


Published: February 1997
First available in Project Euclid: 10 October 2002

zbMATH: 0871.62040
MathSciNet: MR1429931
Digital Object Identifier: 10.1214/aos/1034276635

Primary: 62G07
Secondary: 62G20, 62G30

Rights: Copyright © 1997 Institute of Mathematical Statistics


Vol.25 • No. 1 • February 1997
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