175 – Contributed Poster Presentations: Section on Statistical Learning and Data Science
Spline Density Estimation and Inference with Model-Based Penalties
Jian Shi
University of California
Anna Liu
University of Massachusetts
Yuedong Wang
University of California
In this paper we propose model-based penalties for smoothing spline density estimation and inference. These model-based penalties incorporate indefi nite prior knowledge that the density is close to, but not necessarily in a family of distributions. We will use the Pearson and generalization of the generalized inverse Gaussian families to illustrate the derivation of penalties and reproducing kernels. We also propose new inference procedures to test the hypothesis that the density belongs to a speci fic family of distributions. We conduct extensive simulations to show that the model-based penalties can substantially reduce both bias and variance in the decomposition of the Kullback-Leibler distance, and the new inference procedures are more powerful than some existing ones.