Perform a multiple support test controlling the family-wise error rate (FWER) using the procedure described in Stange, Bodnar, Dickhaus (2015).
fwer.support_test(sample, theta, alpha = 3, beta = 4,
boot.reps = NULL, sigLevel = 0.05)The observed sample (a matrix whose columsn are the observations)
The hypothesized scale theta=c\((\vartheta_1^*,\cdots,\vartheta_m^*\))
First shape parameter of the Beta margins
Second shape parameter of the Beta margins
number of bootstrap repetitions for estimating the parameter \(\eta\) of the Gumbel copula. If this parameter is NULL then \(\eta\) is estimated from Kendalls tau and no bootstrap is performed.
The desired significance level
list l, where
l$statistic contains the values of the test statistics,
l$critvalues are the calibrated critical values,
l$test contains the test decisions,
l$etahat is estimated parameter of the Gumbel copula
The test is performed assuming an i.i.d. sample \(X_1,\cdots,X_n\) which has the stochastic representation $$X_{i,j}=\vartheta_j Z_j$$ where \(Z_j\) takes values in \([0,1]\) and which is distributed according to a Gumbel copula with Beta margins. The test simultaneously tests the hypotheses \(H_{0,j}: \vartheta_j \le \vartheta_j^*\) versus the corresponding alternatives \(H_{1,j}: \vartheta_j>\vartheta_j^*\).
For usage examples and figure reproduction see vignette('fwer-support-test',package='MHTcop').
Note: If the copula is only in the domain of attraction of the Gumbel copula (but not a Gumbel copula) then it is necessary to pass the
number of boot strap repetitions boot.reps as an additional parameter since the non-bootstrapped parameter estimate would not be consistent.
J. Stange, T. Bodnar and T. Dickhaus (2015). Uncertainty quantification for the family-wise error rate in multivariate copula models. AStA Advances in Statistical Analysis 99.3 (2015): 281-310.