2023/01/18 by Nirian Martín, Martin, Nirian
Decision Sciences · Mathematics · #Advanced Statistical Methods and Models #FOS: Computer and information sciences #FOS: Mathematics #Methodology (stat.ME) #Multi-Criteria Decision Making #Statistics Theory (math.ST)
paper · pdf · doi:10.48550/arxiv.2301.07245
openalex publication_date 2023/01/18 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In Econometrics, the Breusch-Pagan test-statistic has become an iconic application of the Lagrange multipliers (LM) test. We shall introduce beta-score LM tests for heteroscedasticity in linear regression models, which trades-off the degree of robustness and efficiency is through a tuning parameter beta>=0, being beta =0 the classical Breusch-Pagan test-statistic, the most efficient one under absence of outliers. A very elegant expression is obtained, with an appealing least squares interpretation. The construction of the test-statistic is performed extending the methodology of Basu et al. (2022) from identically distributed to non-identically distributed individuals, for composite null hypotheses. Detailed theoretical justifications about robustness and efficiency properties are given, all of them under normality. A modified version is derived, the Koenker's beta-score test-statistic.