In spline regression models, the smoothness of the tted model depends on the knots via their location and how many knots there are. An alternative to knot selection is to keep all the knots, but to restrict their in uence on the tted model, that is, to constrain the values of these coe cients which correspond to the spline basis functions. For example, we can bound the squared L2 norm by some c...

We propose a new method for model selection and model fitting in nonparametric regression models, in the framework of smoothing spline ANOVA. The “COSSO” is a method of regularization with the penalty functional being the sum of component norms, instead of the squared norm employed in the traditional smoothing spline method. The COSSO provides a unified framework for several recent proposals fo...

We propose a new method for model selection and model fitting in multivariate nonparametric regression models, in the framework of smoothing spline ANOVA. The “COSSO” is a method of regularization with the penalty functional being the sum of component norms, instead of the squared norm employed in the traditional smoothing spline method. The COSSO provides a unified framework for several recent...

In many regression applications the independent variable is measured with error. When this happens, conventional parametric and nonparametric regression techniques are no longer valid. We consider two different approaches to nonparametric regression. The first uses the SIMEX method and makes no assumption about the distribution of the unobserved error–prone predictor. For this approach we deriv...

A frequency interpretation of Bayesian "confidence" intervals for smoothing splines. Abstract The frequency properties of Wahba's Bayesian "confidence" intervals for smoothing splines are investigated by a large sample approximation and by a simulation study. When the coverage probabilities for these pointwise confidence intervals is averaged across the observation points, we explain why the av...

The P-splines of Eilers andMarx (Stat Sci 11:89– 121, 1996) combine aB-spline basis with a discrete quadratic penalty on the basis coefficients, to produce a reduced rank spline like smoother. P-splines have three properties that make them very popular as reduced rank smoothers: (i) the basis and the penalty are sparse, enabling efficient computation, especially for Bayesian stochastic simulati...