# Boootstrap multiple testing method of Romano & Wolf (2005) for correlations, with stepdown procedure. Multiple testing method based on the evaluation of quantile by bootstrap in the initial dataset (Romano & Wolf (2005)), with stepdown procedure. ```r BootRWCor_SD( data, alpha = 0.05, stat_test = "empirical", Nboot = 1000, vect = FALSE, logical = TRUE, arr.ind = FALSE ) ``` ## Arguments - `data`: matrix of observations - `alpha`: level of multiple testing - `stat_test`: 4 test statistics are available: - **'empirical'**: $\sqrt{n}*abs(corr)$ - **'fisher'**: $\sqrt{n-3}*1/2*\log( (1+corr)/(1-corr) )$ - **'student'**: $\sqrt{n-2}*abs(corr)/\sqrt(1-corr^2)$ - **'2nd.order'**: $\sqrt{n}*mean(Y)/sd(Y)$ with $Y=(X_i-mean(X_i))(X_j-mean(X_j))$ - `Nboot`: number of iterations for Bootstrap quantile evaluation - `vect`: if TRUE returns a vector of TRUE/FALSE values, corresponding to `vectorize(cor(data))`; if FALSE, returns an array containing TRUE/FALSE values for each entry of the correlation matrix - `logical`: if TRUE, returns either a vector or a matrix where each element is equal to TRUE if the corresponding null hypothesis is rejected, and to FALSE if it is not rejected if FALSE, returns a list of successive p-values : element [[i+1]] of the list giving the p-values evaluated on the non-rejected hypothesis at step [[i]]; p-values are either as a vector or a list depending on `vect` - `arr.ind`: if TRUE, returns the indexes of the significant correlations, with respect to level alpha ## Returns Returns * logicals, equal to TRUE if the corresponding element of the statistic vector is rejected, as a vector or a matrix depending of the value of `vect`, * an array containing indexes $\lbrace(i,j),\,i\

BootRWCor_SD function