# Conducts the serial independence test (WISE) based on a similarity matrix Returns the p-value of WISE, the squared test statistic, and related quantities (the chi-square critical value, permutation mean, permutation variance). ```r wise_test(sim, dependence = "proximity", alpha = 0.05, weight = NULL, h = 4) ``` ## Arguments - `sim`: an n by n similarity matrix, typically generated from wise_sim(). - `dependence`: design for the weight matrix W: if "proximity", $W_{ij} = (1 / (|i - j|^2 + 1))-1$; if "periodicity", then $W_{ij} = |cos(|i-j|\pi/h)|-1$; If "customized", users should input their self-defined weight matrix through the parameter "weight". The default is "proximity" - `alpha`: the nominal significance level (default is 0.05). - `weight`: an n by n weight matrix with zero diagonal (only used if dependence = "customized"). - `h`: the estimated periodicity (default is 4). The parameter is used only if dependence = "periodicity". ## Returns A list containing: - **p_value**: The p-value of the test. - **test_statistic_sq**: The value of the squared test statistic. - **critical_value**: The chi-square critical value at the given significance level. - **t**: The unstandardized test statistic. - **permutation_mean**: The mean of t under the permutation null. - **permutation_variance**: The variance of t under the permutation null. ## Examples ```r library(MASS) n <- 100 p <- 50 # Example 1: iid data set.seed(123) data_iid <- mvrnorm(n = n, mu = rep(0, p) , Sigma = diag(p)) wise_test( wise_sim(data_iid, measure = "distance", metric = "manhattan"), dependence = "proximity", alpha = 0.05 ) # Example 2: AR(1) set.seed(123) data_ar <- matrix(0, nrow = n, ncol = p) error <- mvrnorm(n = n, mu = rep(0,p), Sigma = diag(p)) data_ar[1,] <- error[1,] phi <- 0.1 * diag(p) for (t in 2:n) { data_ar[t, ] <- phi %*% data_ar[t - 1, ] + error[t,] } wise_test( wise_sim(data_ar, measure = "distance", metric = "manhattan"), dependence = "proximity", alpha = 0.05 ) # Example 3: NMA(2) set.seed(123) data_nma <- matrix(0, nrow = n, ncol = p) error <- mvrnorm(n = n, mu = rep(0,p), Sigma = diag(p)) data_nma[1:2, 1:p] <-error[1:2,1:p] for (i in 3:n) { data_nma[i, ] <- error[i,]*error[i-1,]*error[i-2,] } wise_test( wise_sim(data_nma, measure = "distance", metric = "manhattan"), dependence = "proximity", alpha = 0.05 ) ```

wise_test function