2020/01/08 by Marc Ditzhaus, Daniel Gaigall, Ditzhaus, Marc +1
Computer Science · Economics, Econometrics and Finance · Mathematics · #Bayesian Methods and Mixture Models #FOS: Computer and information sciences #FOS: Mathematics #Financial Risk and Volatility Modeling #Methodology (stat.ME) #Statistical Methods and Inference #Statistics Theory (math.ST)
paper · pdf · doi:10.48550/arxiv.2001.02488
openalex publication_date 2020/01/08 · openalex created_date 2022/07/26 · openalex updated_date 2026/07/28
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.