A robust adaptive-to-model enhancement test for parametric single-index models

TL;DR

This paper introduces a robust, adaptive test for parametric single-index models that effectively handles outliers, reduces dimensionality issues, and adapts to alternative models, with demonstrated superior performance through simulations and real data.

Contribution

It proposes a new outlier-robust, adaptive testing method that leverages dimension reduction and is effective against general alternatives in single-index models.

Findings

Bounded influence function ensures robustness to outliers.

The test adapts to alternative models when the null is false.

Simulation and real data show improved performance over existing methods.

Abstract

In the research on checking whether the underlying model is of parametric single-index structure with outliers in observations, the purpose of this paper is two-fold. First, a test that is robust against outliers is suggested. The Hampel's second-order influence function of the test statistic is proved to be bounded. Second, the test fully uses the dimension reduction structure of the hypothetical model and automatically adapts to alternative models when the null hypothesis is false. Thus, the test can greatly overcome the dimensionality problem and is still omnibus against general alternative models. The performance of the test is demonstrated by both Monte Carlo simulation studies and an application to a real dataset.