We revisit the family of goodness-of-fit tests for exponentiality based on the mean residual life time proposed by Baringhaus & Henze (2008). We motivate the test statistic by a characterisation of Shanbhag (1970) and provide an alternative representation, which leads to simple and short proofs for the known theory and an easy to access covariance structure of the limiting Gaussian process under the null hypothesis. Explicit formulas for the eigenvalues and eigenfunctions of the operator associated with the limit covariance are derived using results on weighted Brownian bridges. In addition we provide further asymptotic theory under fixed alternatives and derive approximate Bahadur efficiencies, which provide an insight into the choice of the tuning parameter with regard to the power performance of the tests.

翻译：本文重新探讨了由Baringhaus & Henze (2008)提出的基于均值剩余寿命的指数性拟合优度检验族。我们通过Shanbhag (1970)的特征刻画来推导检验统计量，并给出另一种表达形式。该表达形式不仅为现有理论提供了简洁的证明，还揭示了原假设下极限高斯过程协方差结构的简便计算方法。利用加权布朗桥的相关结果，推导出与极限协方差关联算子的特征值和特征函数的显式表达式。此外，我们建立了固定备择假设下的渐近理论，并计算了近似Bahadur效率，这为从检验效能角度选择调节参数提供了理论依据。