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ON A TEST FOR EXPONENTIALITY AGAINST LAPLACE ORDER DOMINANCE

机译：反对Laplace Order优势的指数测试

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摘要

In a recent paper, Basu and Mitra (2002) introduced a class of tests for exponentiality against the non-parametric class L of life distributions. The test statistics are fractional sample moments. In a simulation study, the tests show a remarkable behavior: when performed on a nominal level of 5%, each of the tests always accepted the null hypothesis of exponentiality if the underlying data came from an exponential distribution. Furthermore, power of the tests was very low compared to other procedures designed for the same testing situation. It is the aim of this paper to show that the reasons for this behavior are an incorrectly stated asymptotic distribution, a slow convergence of the finite sample distributions of the test statistics to their limit distribution, and, to a minor extent, the dependence of the proposed tests on the choice of parameter values. To this end, we derive the limit distributions of the test statistics in case of a general underlying distribution and the local approximate Bahadur efficiency of the tests against several parametric families of alternatives to exponentiality. Additionally, the finite sample behavior of the tests is examined by means of a simulation study. Further, we enlarge the proposed class of tests by extending some characterization of exponentiality within the L-class.
机译：在最近的一篇论文中，Basu和Mitra（2002）引入了一类针对生命分布的非参数L类的指数检验。测试统计数据是分数样本矩。在模拟研究中，测试显示出显着的行为：以5％的名义水平执行时，如果基础数据来自指数分布，则每个测试始终接受指数的零假设。此外，与针对相同测试情况设计的其他程序相比，这些测试的功能非常低。本文的目的是表明这种现象的原因是：错误地陈述了渐近分布，测试统计量的有限样本分布缓慢收敛到其极限分布，以及在较小程度上依赖于建议的关于参数值选择的测试。为此，我们得出了一般基础分布的情况下检验统计量的极限分布，以及针对指数替代的几个参数族的检验的局部近似Bahadur效率。此外，还通过模拟研究来检验测试的有限样本行为。此外，我们通过扩展L类中的指数特性来扩展建议的测试类。

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