Spatially-adaptive penalties for spline fitting Academic Article uri icon

abstract

  • The paper studies spline fitting with a roughness penalty that adapts to spatial heterogeneity in the regression function. The estimates are pth degree piecewise polynomials with p - 1 continuous derivatives. A large and fixed number of knots is used and smoothing is achieved by putting a quadratic penalty on the jumps of the pth derivative at the knots. To be spatially adaptive, the logarithm of the penalty is itself a linear spline but with relatively few knots and with values at the knots chosen to minimize the generalized cross validation (GCV) criterion. This locally-adaptive spline estimator is compared with other spline estimators in the literature such as cubic smoothing splines and knot-selection techniques for least squares regression. Our estimator can be interpreted as an empirical Bayes estimate for a prior allowing spatial heterogeneity. In cases of spatially heterogeneous regression functions, empirical Bayes confidence intervals using this prior achieve better pointwise coverage probabilities than confidence intervals based on a global-penalty parameter. The method is developed first for univariate models and then extended to additive models. Australian Statistical Publishing Association Inc. 2000. Published by Blackwell Publishers Ltd.

published proceedings

  • AUSTRALIAN & NEW ZEALAND JOURNAL OF STATISTICS

author list (cited authors)

  • Ruppert, D., & Carroll, R. J.

citation count

  • 159

complete list of authors

  • Ruppert, D||Carroll, RJ

publication date

  • June 2000

publisher