Gaussian dependence structure pairwise goodness-of-fit testing based on conditional covariance and the 20/60/20 rule
arxiv(2024)
摘要
We present a novel data-oriented statistical framework that assesses the
presumed Gaussian dependence structure in a pairwise setting. This refers to
both multivariate normality and normal copula goodness-of-fit testing. The
proposed test clusters the data according to the 20/60/20 rule and confronts
conditional covariance (or correlation) estimates on the obtained subsets. The
corresponding test statistic has a natural practical interpretation, desirable
statistical properties, and asymptotic pivotal distribution under the
multivariate normality assumption. We illustrate the usefulness of the
introduced framework using extensive power simulation studies and show that our
approach outperforms popular benchmark alternatives. Also, we apply the
proposed methodology to commodities market data.
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