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首页> 外文期刊>Journal of nonparametric statistics >Le Cam optimal tests for symmetry against Ferreira and Steel's general skewed distributions
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Le Cam optimal tests for symmetry against Ferreira and Steel's general skewed distributions

机译：Le Cam针对Ferreira和Steel一般偏斜分布的对称性的最佳测试

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摘要

When testing symmetry of a univariate density, (parametric classes of) densities skewed by means of the general probability transform introduced in Ferreira and Steel [A constructive representation of univariate skewed distributions, J. Amer. Statist. Assoc. 101 (2006), pp. 823-829] are appealing alternatives. This paper first proposes parametric tests of symmetry (about a specified centre) that are locally and asymptotically optimal (in the Le Cam sense) against such alternatives. To improve on these parametric tests, which are valid under well-specified density types only, we turn them into semiparametric tests, either by using a standard studentisation approach or by resorting to the invariance principle. The second approach leads to robust yet efficient signed-rank tests, which include the celebrated sign and Wilcoxon tests as special cases, and turn out to be Le Cam optimal irrespective of the underlying original symmetric density. Optimality, however, is only achieved under well-specified 'skewing mechanisms', and we therefore evaluate the overall performances of our tests by deriving their asymptotic relative efficiencies with respect to the classical test of skewness. A Monte-Carlo study confirms the asymptotic results.
机译：当测试单变量密度的对称性时，（在参数的参数类别中）通过费雷拉和斯蒂尔引入的一般概率变换[密度的参数化构造，J。Amer。统计员。副会长101（2006），第823-829页]。本文首先提出了关于对称性的参数测试（在指定的中心附近），针对这些选择，它们在局部和渐近最优（在Le Cam意义上）。为了改进这些参数测试（仅在指定的密度类型下有效），我们可以通过使用标准的学生化方法或采用不变性原理将它们转换为半参数测试。第二种方法导致稳健而有效的符号秩检验，其中包括著名的符号检验和Wilcoxon检验作为特例，并且无论其潜在的原始对称密度如何，它都是Le Cam最佳的。然而，最优性只能在明确规定的“倾斜机制”下实现，因此，我们通过得出相对于经典偏度测试的渐近相对效率来评估测试的整体性能。蒙特卡洛研究证实了渐近结果。

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