Higher-order asymptotic refinements in a multivariate regression model with general parameterization

Abstract

This paper derives a general Bartlett correction formula to improve the inference based on the likelihood ratio test in a multivariate model under a quite general parameterization, where the mean vector and the variance-covariance matrix can share the same vector of parameters. This approach includes a number of models as special cases such as non-linear regression models, errors-in-variables models, mixed-effects models with non-linear fixed effects, and mixtures of the previous models. We also employ the Skovgaard adjustment to the likelihood ratio statistic in this class of multivariate models and derive a general expression of the correction factor based on Skovgaard approach. Monte Carlo simulation experiments are carried out to verify the performance of the improved tests, and the numerical results confirm that the modified tests are more reliable than the usual likelihood ratio test. Applications to real data are also presented for illustrative purposes.

Keywords:

• Bartlett correction
• likelihood ratio test
• parametric inference
• Skovgaard adjustment

Mathematics Subject classifications:

• 62F03
• 62F05
• 62F10

Acknowledgments

The authors would like to thank the anonymous reviewers for the insightful comments and suggestions which have significantly improved the current work.

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

Tatiane Melo and Tiago Vargas gratefully acknowledge the financial support of the Brazilian agency FAPEG [grant number 201410267001779]. Artur Lemonte gratefully acknowledges the financial support of the Brazilian agency Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq) [grant number 303554/2022–3].