On wavelets to select the parametric form of a regression model

TL;DR

This paper explores using wavelet regression as a non-parametric auxiliary tool to identify the true parametric form of a regression model, especially for nonlinear and generalized linear models, enhancing model selection without strict assumptions.

Contribution

It introduces a wavelet-based method for selecting the true parametric model among candidates, offering a simple, assumption-free alternative for regression model choice.

Findings

Wavelet method accurately identifies the true model in various scenarios.

The approach performs well on real data applications.

It provides a non-parametric, assumption-light model selection technique.

Abstract

Let Y be a response variable related with a set of explanatory variables and let f1, f2, ..., fk be a set of the parametric forms representing a set of candidate's model. Let f* be the true model among the set of k plausible models. We discuss in this paper the use of wavelet regression method as auxiliary for the choice of the "true" parametric form of a regression model, particularly, for the cases of nonlinear regression and generalized linear models. The use of a non-parametric method for the choice of the more appropriate parametric equation in regression problems would be interesting in practice due to the simplicity and because the probabilistic assumptions are not required. We evaluate the performance of the proposed wavelet procedure based on the true classification rate of the correct parametric form among a range of k candidate models, taking into account a wide ranges of scenarios and configurations as well as in real data set applications.