Doubly-nonparametric generalized additive models

TL;DR

This paper introduces a flexible extension of generalized additive models that allows both the mean functions and response distribution to be nonparametric, enhancing modeling flexibility and diagnostic capabilities.

Contribution

It develops a doubly-nonparametric framework for generalized additive models, allowing nonparametric modeling of both mean and response distribution, and demonstrates its effectiveness through simulations and real data examples.

Findings

Flexible modeling of mean and response distribution.

Good finite-sample performance in simulations.

Effective for data analysis and model diagnostics.

Abstract

The popular generalized additive model framework is extended to allow both the mean curves and the response distribution to be nonparametric. The approach is demonstrated to be a flexible yet parsimonious tool for data analysis in its own right, as well as being a useful tool for model selection and diagnosis in the classical generalized additive model framework. Finite-sample performance of the method is examined via various simulation settings and the method is illustrated on two data analysis examples.