Robust likelihood inferences about regression parameters for general bivariate continuous data

Abstract

This paper introduces a way of modifying the bivariate normal likelihood function. One can use the adjusted likelihood to generate valid likelihood inferences for the regression parameter of interest, even if the bivariate normal assumption is fallacious. The retained asymptotic legitimacy requires no knowledge of the true underlying joint distributions so long as their second moments exist. The extension to the multivariate situations is straightforward in theory and yet appears to be arduous computationally. Nevertheless, it is illustrated that the implementation of this seemingly sophisticated procedure is almost effortless needing only outputs from existing statistical software. The efficacy of the proposed parametric approach is demonstrated via simulations.