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.
翻译:在计量经济学中,Breusch-Pagan测试-统计学已成为Lagrange 乘数(LM)测试的标志性应用。我们将在线性回归模型中引入乙核LM测试,其稳健度和效率的取舍是通过调试参数贝塔 ⁇ 0, 即贝塔=0, 古典Breusch-Pagan测试-统计学, 是在没有离子的情况下最有效率的。 获得了一种非常优雅的表达, 其解释最差。 测试- 统计学的构建将Basu等人(2022年)的方法从相同分布到非身份分布的个人(2022年)的方法延伸至非身份分布, 综合无损假体。 给出了关于稳健性和效率属性的详细理论依据, 全部都在正常状态下。 修改版本后产生, Koenker的乙核测试统计学。