基于Arnold-Villasenor特征的指数性检验及其效率
Tests of exponentiality based on Arnold-Villasenor characterization, and their efficiencies
摘要：
我们提出了两个家庭的无标度指数测试的基础上最近的表征指数Arnold和Villasenor。检验统计量基于U-经验分布函数的适当泛函。积分统计族可以简化为具有相对简单的非退化核的V-或U-统计。它们是渐近正态的，并且在常见的替代方案下具有相当高的局部Bahadur效率。这种效率与新的测试模拟功率进行比较。另一方面，Kolmogorov型测试表明非常低的当地Bahadur效率和相当温和的权力，为共同的替代品，几乎不能推荐给从业者。我们还探讨了新的测试的局部渐近最优性的条件，并描述了两个家庭的特殊的“最有利的”替代品的测试是完全有效的。
英文摘要：
We propose two families of scale-free exponentiality tests based on the recent characterization of exponentiality by Arnold and Villasenor. The test statistics are based on suitable functionals of U-empirical distribution functions. The family of integral statistics can be reduced to V- or U-statistics with relatively simple non-degenerate kernels. They are asymptotically normal and have reasonably high local Bahadur efficiency under common alternatives. This efficiency is compared with simulated powers of new tests. On the other hand, the Kolmogorov type tests demonstrate very low local Bahadur efficiency and rather moderate power for common alternatives,and can hardly be recommended to practitioners. We also explore the conditions of local asymptotic optimality of new tests and describe for both families special "most favorable" alternatives for which the tests are fully efficient.
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