Smoothing Spline Estimation of Variance Functions

Smoothing Spline Estimation of Variance Functions

This article considers spline smoothing of variance functions. We focus on selection of smoothing parameters and develop three direct data-driven methods: unbiased risk (UBR), generalized approximate cross validation (GACV) and generalized maximum likelihood (GML). In addition to guaranteed convergence, simulations show that these direct methods perform better than existing indirect UBR, genera...

Smoothing by Spline Functions

Likelihood and Smoothing Spline Analysis of Variance

We discuss a class of methods for the problem of `soft' classi cation in supervised learning. In `hard' classi cation, it is assumed that any two examples with the same attribute vector will always be in the same class, (or have the same outcome), whereas in `soft' classi cation, two examples with the same attribute vector do not necessarily have the same outcome, but the probability of a parti...

Odds ratio estimation in Bernoulli smoothing spline analysis-of- variance models

Wahba and co-workers introduced the smoothing spline analysis-of-variance (SS ANOVA) method for data from exponential families. In this paper, we estimate the odds ratios based on an SS ANOVA model for binary data and construct Bayesian confidence intervals. We give a calculation using a real data set from the Wisconsin epidemiological study of diabetic retinopathy. We conduct simulations to ev...

Smoothing Noisy Data with Spline Functions *

I t is shown how to choose the smoothing parameter when a smoothing periodic spline of degree 2m -1 is used to reconstruct a smooth periodic curve from noisy ordinate data. The noise is assumed "white" , and the true curve is assumed to be in the Sobolev space W,(*ra) of periodic functions with absolutely continuous v-th derivative, v = 0, t . . . . . 2 m I and square integrable 2m-th derivativ...