论文标题
在希尔伯特空间中测试边际同质性，并向股票市场收益申请
Testing marginal homogeneity in Hilbert spaces with applications to stock market returns
论文作者
论文摘要
本文考虑了一个配对的数据框架，并讨论了双变量高维或功能数据的边际同质性问题。可以将相关的测试问题赋予更通用的设置，以使成对的随机变量在一般的希尔伯特空间中采用值。为了解决此问题，应用了Cramer-Von-Mises类型测试统计量，并建议进行自举程序以获得临界值，最后进行一致的测试。可以得出引导程序测试的所需特性，在替代方面的零假设和一致性下，它们是渐近的精确性。模拟显示了有限样本案例中测试的质量。可能的应用是根据功能数据的两个可能依赖股票市场收益的比较。该方法是根据不同股票市场指数的历史数据来证明的。
The paper considers a paired data framework and discuss the question of marginal homogeneity of bivariate high dimensional or functional data. The related testing problem can be endowed into a more general setting for paired random variables taking values in a general Hilbert space. To address this problem, a Cramer-von-Mises type test statistic is applied and a bootstrap procedure is suggested to obtain critical values and finally a consistent test. The desired properties of a bootstrap test can be derived, that are asymptotic exactness under the null hypothesis and consistency under alternatives. Simulations show the quality of the test in the finite sample case. A possible application is the comparison of two possibly dependent stock market returns on the basis of functional data. The approach is demonstrated on the basis of historical data for different stock market indices.
