Penalized Log Likelihood Density Estimation, via Smoothing-Spline ANOVA and ranGACV - Comments to Hansen and Kooperberg, ‘Spline Adaptation in Extended Linear Models’

We thank Hansen and Kooperberg (HK) for an interesting paper discussing model selection methods in the context of Extended Linear Models. We comment on their univariate density estimation studies, which maximize the log likelihood in a low dimensional linear space. They consider spline bases for this space and consider greedy and Bayesian methods for choosing the knots. We describe a penalized log likelihood univariate density estimate, and compare the estimate to those studied by HK. Then we describe the multivariate version of our estimate, based on a Smoothing Spline ANOVA model. A randomized Generalized Approximate Cross Validation estimate for the smoothing parameters is obtained and an example is given. This represents work in progress.