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首页> 外文期刊>Journal of Econometrics >On Distribution-Free Goodness-of-Fit Testing of Exponentiality.
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On Distribution-Free Goodness-of-Fit Testing of Exponentiality.

机译：关于指数的无分布拟合优度测试。

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There is a need to test the hypothesis of exponentiality against a wide variety of alternative hypotheses, across many areas of economics and finance. Local or contiguous alternatives are the closest alternatives against which it is still possible to have some power. Hence goodness-of-fit tests should have some power against all, or a huge majority, of local alternatives. Such tests are often based on nonlinear statistics, with a complicated asymptotic null distribution. Thus a second desirable property of a goodness-of-fit test is that its statistic will be asymptotically distribution free. We suggest a whole class of goodness-of-fit tests with both of these properties, by constructing a new version of empirical process that weakly converges to a standard Brownian motion under the hypothesis of exponentiality. All statistics based on this process will asymptotically behave as statistics from a standard Brownian motion and so will be asymptotically distribution free. We show the form of transformation is especially simple in the case of exponentiality. Surprisingly there are only two asymptotically distribution free versions of empirical process for this problem, and only this one has a convenient limit distribution. Many tests of exponentiality have been suggested based on asymptotically linear functionals from the empirical process. We illustrate none of these can be used as goodness-of-fit tests, contrary to some previous recommendations. Of considerable interest is that a selection of well-known statistics all lead to the same test asymptotically, with negligible asymptotic power against a great majority of local alternatives. Finally, we present an extension of our approach that solves the problem of multiple testing, both for exponentiality and for other, more general hypotheses.
机译：有必要在经济和金融的许多领域中，针对各种各样的替代假设检验指数假设。本地或连续的替代方案是最接近的替代方案，仍然可以对它进行一些处理。因此，拟合优度测试应该对所有或绝大多数本地替代品具有一定的影响力。这种测试通常基于非线性统计，具有复杂的渐近零分布。因此，拟合优度检验的第二个理想属性是其统计量将渐近分布。通过构建新的经验过程的新版本，我们提出了一类同时具有这两个属性的拟合优度检验，该新版本的经验过程在指数假设下弱收敛至标准布朗运动。基于此过程的所有统计量将渐近地表现为标准布朗运动的统计量，因此将无渐近分布。我们证明了在指数情况下变换的形式特别简单。令人惊讶的是，对于该问题，只有两个渐近分布的经验过程自由版本，并且只有一个具有方便的极限分布。根据经验过程，已提出基于渐近线性泛函的许多指数测试。我们举例说明，与先前的某些建议相反，这些方法均不能用作拟合优度测试。相当有趣的是，所有知名统计数据的选择都渐近地导致了相同的检验，并且相对于大多数本地替代品而言，其渐近力可以忽略不计。最后，我们提出了方法的扩展，解决了指数和其他更普遍假设的多重测试问题。

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