Comparing Two Approaches in Heteroscedastic Regression Models

TL;DR

This paper demonstrates that two recent methods for testing coefficient equality in heteroscedastic regression models are statistically equivalent, unifying their theoretical foundations and extending the result to one-way ANOVA.

Contribution

It proves the equivalence of the generalized test and fiducial approaches, clarifying their relationship and applicability in heteroscedastic regression and ANOVA.

Findings

The two approaches are statistically identical in distribution.

The equivalence holds for one-way ANOVA.

This unification simplifies the choice of testing methods.

Abstract

Recently, a generalized test approach is proposed by Sadooghi-alvandi et al. (2016) and a fiducial approach is proposed by Xu and Li (2018) to test the equality of coefficients in several regression models with unequal variances. In this paper, it is shown that the considered quantities in these approaches are identically distributed and therefore, these approaches are same. Also, this result satisfies for the one-way ANOVA problem.