Perform a multiple (two-sided) z-test controlling the family-wise error rate (FWER) using the procedure described in Stange, Bodnar, Dickhaus (2015).
fwer.ztest(sample, mu, sigma = NULL, sigLevel = 0.05)The observed sample
The mean \(\mu^*\)
The estimated covariance matrix (the copula parameter). If it is omitted it will be estimated from an AR(1) model
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
Let \(X_1,\cdots,X_n\) denote an i.i.d. sample with values in \({\rm I\!R}^m\). Furthermore let \(\mu_j={\rm I\!E}[X_{1,j}]\) be the component-wise expectations. Then the multiple (two-sided) z-test simultaneously tests the hypotheses \(H_{0,j}: \mu_j = \mu_j^*\) versus the corresponding alternatives \(H_{1,j}: \mu_j\not=\mu_j^*\).
For usage examples and figure reproduction see vignette('fwer-ztest',package='MHTcop').
Note: If the parameter sigma is passed it needs to be a consistent estimate of the covariance matrix of \(X_1\).
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.