fwer.support_test: Copula-based multiple support test which controlls the FWER
In MHTcop: Tests Controlling the FDR / FWER under Certain Copula Models

Description Usage Arguments Details Value References

Perform a multiple support test controlling the family-wise error rate (FWER) using the procedure described in Stange, Bodnar, Dickhaus (2015).

1 2	fwer.support_test(sample, theta, alpha = 3, beta = 4, boot.reps = NULL, sigLevel = 0.05)

`sample`	The observed sample (a matrix whose columsn are the observations)
`theta`	The hypothesized scale `theta=c`(\vartheta_1^,\cdots,\vartheta_m^`)`
`alpha`	First shape parameter of the Beta margins
`beta`	Second shape parameter of the Beta margins
`boot.reps`	number of bootstrap repetitions for estimating the parameter η of the Gumbel copula. If this parameter is NULL then η is estimated from Kendalls tau and no bootstrap is performed.
`sigLevel`	The desired significance level

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 ≤ \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.

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

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.

MHTcop documentation built on May 2, 2019, 7:59 a.m.