Rank tests for corrupted linear models

TL;DR

This paper demonstrates that rank-based tests outperform classical parametric tests in corrupted linear models, such as measurement error or semi-parametric models, especially when regularity assumptions are violated.

Contribution

It introduces adapted rank-based tests for corrupted linear models and shows their superior performance over traditional methods through numerical and real data analyses.

Findings

Rank-based tests outperform classical tests in corrupted models.

Incorporating rank analysis of covariance improves power.

Numerical studies confirm the effectiveness of the proposed methods.

Abstract

For some variants of regression models, including partial, measurement error or error-in-variables, latent effects, semi-parametric and otherwise corrupted linear models, the classical parametric tests generally do not perform well. Various modifications and generalizations considered extensively in the literature rests on stringent regularity assumptions which are not likely to be tenable in many applications. However, in such non-standard cases, rank based tests can be adapted better, and further, incorporation of rank analysis of covariance tools enhance their power-efficiency. Numerical studies and a real data illustration show the superiority of rank based inference in such corrupted linear models.