Novel specification tests for additive concurrent model formulation based on martingale difference divergence

TL;DR

This paper introduces new significance tests for additive concurrent models using martingale difference divergence, enabling model validation and covariate selection without complex preliminary estimation or tuning parameters.

Contribution

It develops novel, model-free tests based on martingale difference divergence for assessing conditional mean independence in additive concurrent models.

Findings

Tests effectively detect dependence in simulations

Bootstrap method accurately computes p-values

Applied to real datasets with successful results

Abstract

Novel significance tests are proposed for the quite general additive concurrent model formulation without the need of model, error structure preliminary estimation or the use of tuning parameters. Making use of the martingale difference divergence coefficient, we propose new tests to measure the conditional mean independence in the concurrent model framework taking under consideration all observed time instants. In particular, global dependence tests to quantify the effect of a group of covariates in the response as well as partial ones to apply covariates selection are introduced. Their asymptotic distribution is obtained on each case and a bootstrap algorithm is proposed to compute its p-values in practice. These new procedures are tested by means of simulation studies and some real datasets analysis.