AMlet, RAMlet, and GAMlet: Automatic Nonlinear Fitting of Additive Models, Robust and Generalized, With Wavelets

Abstract

A simple and yet powerful method is presented to estimate nonlinearly and nonparametrically the components of additive models using wavelets. The estimator enjoys the good statistical and computational properties of the Waveshrink scatterplot smoother and it can be efficiently computed using the block coordinate relaxation optimization technique. A rule for the automatic selection of the smoothing parameters, suitable for data mining of large datasets, is derived. The wavelet-based method is then extended to estimate generalized additive models. A primal-dual log-barrier interior point algorithm is proposed to solve the corresponding convex programming problem. Based on an asymptotic analysis, a rule for selecting the smoothing parameters is derived, enabling the estimator to be fully automated in practice. We illustrate the finite sample property with a Gaussian and a Poisson simulation.

Key Words:

• (Generalized) additive models
• Convex programming
• Data mining
• Interior point algorithm
• Regularized likelihood
• Relaxation algorithm
• Signal denoising
• Universal smoothing parameter