Degenerate $$U$$- and $$V$$-statistics under ergodicity: asymptotics, bootstrap and applications in statistics
Degenerate $$U$$- and $$V$$-statistics under ergodicity: asymptotics, bootstrap and applications in statistics
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遍历性下的退化 $$U$$- 和 $$V$$-统计：渐近、自举和统计中的应用
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发表时间：
2013
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通讯作者：
Michael H. Neumann
中科院分区：
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作者：
Anne Leucht;Michael H. Neumann
我们导出了平稳和遍历随机变量的退化$$U$$ -和$$V$$ -统计量的渐近分布。这些类型的统计自然表现为测试统计的近似值。由于极限变量结构复杂，通常依赖于未知参数，很难直接得到分位数。因此，在易于验证的条件下，我们证明了$$U$$ -和$$V$$ -统计的基于模型的自举方法的一致性的一般结果。提出了假设检验的三种应用。最后，通过仿真研究说明了基于自举的试验的有限样本行为。
We derive the asymptotic distributions of degenerate $$U$$- and $$V$$-statistics of stationary and ergodic random variables. Statistics of these types naturally appear as approximations of test statistics. Since the limit variables are of complicated structure, typically depending on unknown parameters, quantiles can hardly be obtained directly. Therefore, we prove a general result on the consistency of model-based bootstrap methods for $$U$$- and $$V$$-statistics under easily verifiable conditions. Three applications to hypothesis testing are presented. Finally, the finite sample behavior of the bootstrap-based tests is illustrated by a simulation study.