论文标题
基于平均残留寿命功能的指数测试重新审视
The test of exponentiality based on the mean residual life function revisited
论文作者
论文摘要
我们根据Baringhaus＆Henze（2008）提出的平均剩余寿命，重新审视指数性的拟合优度测试。我们通过Shanbhag（1970）的特征来激励测试统计量，并提供了另一种表示形式，从而为已知理论提供了简单而简短的证明，并且在零假设下限制了高斯过程的易于访问的协方差结构。使用加权布朗尼桥的结果得出了与极限协方差相关的操作员特征值和特征函数的显式公式。此外，我们在固定替代方案下提供了进一步的渐近理论，并得出了近似的巴哈杜尔效率，该效率提供了有关调整参数的选择，就测试的功率性能而言。
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.
