Model checking for generalized linear models: a dimension-reduction model-adaptive approach

TL;DR

This paper introduces a dimension-reduction, model-adaptive testing method for generalized linear models that overcomes the curse of dimensionality, maintaining significance levels and detecting local alternatives efficiently.

Contribution

It proposes a novel dimension-reduction approach that makes local smoothing tests effective for multivariate models, achieving fast detection rates and broad consistency.

Findings

Performs well in simulations compared to existing tests.

Maintains significance level under various conditions.

Successfully applied to real data analysis.

Abstract

Local smoothing testing that is based on multivariate nonparametric regression estimation is one of the main model checking methodologies in the literature. However, relevant tests suffer from the typical curse of dimensionality resulting in slow convergence rates to their limits under the null hypotheses and less deviation from the null under alternatives. This problem leads tests to not well maintain the significance level and to be less sensitive to alternatives. In this paper, a dimension-reduction model-adaptive test is proposed for generalized linear models. The test behaves like a local smoothing test as if the model were univariate, and can be consistent against any global alternatives and can detect local alternatives distinct from the null at a fast rate that existing local smoothing tests can achieve only when the model is univariate. Simulations are carried out to examine the performance of our methodology. A real data analysis is conducted for illustration. The method can readily be extended to global smoothing methodology and other testing problems.