Abstract
We use a recently proposed fast test of copula radial symmetry based on multiplier bootstrap and obtain an equivalent randomization test. The literature shows the statistical superiority of the randomization approach in the bivariate case. We extend the comparison of statistical performance focusing on the high-dimensional regime in a simulation study. We document radial asymmetry in the joint distribution of the percentage changes of sectorial industrial production indices of the European Union.
Highlights
Let Fi(x), i = 1, . . . , d be the marginal cumulative distribution functions (CDFs) of a continuous random vector X = (X1, . . . , Xd)
Before considering the statistical performance, we study the computational performance of the different procedures and report in Table 1, as an example, the running times for the number of observations n = 250 and dimension d = 100, estimated from 1000 replicates, under the Frank copula model, using Matlab on a Windows 10 laptop with an Intel i7-6500U CPU and 8 GB of RAM
It compares in a simulation study with a high number of variables and its computing and statistical performance with the performance of the multiplier bootstrap procedure developed in [19]
Summary
An extensive simulation study shows that the statistical procedure based on Equation (3) has size and power better than the proposal introduced in [17]. The authors of [22], limiting themselves to the bivariate case, propose to approximate the distribution of Equation (3) and other statistics using randomization instead of the multiplier bootstrap. They show better finite sample behavior compared to the use of the multiplier techniques.
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