Abstract #301268

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JSM 2003 Abstract #301268
Activity Number: 210
Type: Contributed
Date/Time: Tuesday, August 5, 2003 : 8:30 AM to 10:20 AM
Sponsor: Section on Nonparametric Statistics
Abstract - #301268
Title: Adaptive Multiorder Penalized Splines
Author(s): Daniel Fink*+ and Martin T. Wells
Companies: Cornell University and Cornell University
Address: 1477 1/2 Slaterville Rd., Ithaca, NY, 14850-6246,
Keywords: smoothing ; regression splines ; changepoints
Abstract:

We develop a nonparametric penalized regression spline that adapts to spatial heterogeneity by constructing a data-based multiorder truncated spline basis. The class of multiorder truncated spline bases allow for jumps in the regression function and its first derivative. The regression function is estimated by adaptively constructing a basis from this class and then fitting the resulting penalized regression spline. This spatially adaptive spline estimator is compared with other spline estimators in the literature such as penalized regression splines with local smoothness penalties, adaptive regression spline techniques, and wavelet procedures. A related variance estimator for spatial heterogeneous signals is introduced. This estimator uses basis economy to differentiate between signal and noise with respect to the spline basis. Variance calibration automatically thresholds the basis economy components and identifies the subset of the data used to estimate the variance. This approach compares favorably with other estimators in simulation tests.

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