# Test the existence of kink effect in the multi-kink quantile regression This function tests the existence of a kink effect in the multi-kink quantile regression. ```r KinkTest( y, thre.x, cont.z, id, tau = 0.5, NB = 200, sparsity = "nid", bandwidth_type = c("Hall-Sheather", "Bofinger", "Chamberlain") ) ``` ## Arguments - `y`: A numeric vector of response. - `thre.x`: A numeric vector of scalar covariate with threshold effect. - `cont.z`: A numeric matrix of design covariates with constant slopes. - `id`: A numeric vector of index used for longitudinal data; can be missing or NULL for iid data. - `tau`: A numeric scalar representing the quantile level (default is 0.5). - `NB`: An integer specifying the resampling times (default is 200). - `sparsity`: The error term type. Specify one from "iid" and "nid" (default is "nid"). - `bandwidth_type`: The bandwidth type. Specify one from "Hall-Sheather", "Bofinger", or "Chamberlain" (default is "Hall-Sheather"). ## Returns A list containing the p-value (pv), the statistic based on the original data (Tn), and the statistics by wild bootstrap (Tn.NB). ## Examples ```r # Example 1: i.i.d data type library(quantreg) n = 200 Z1 <- rexp(n,1) Z2 <- rbinom(n,1,0.5) Z <- cbind(Z1,Z2) epsilon <- rnorm(n,0,1) X <- runif(n,-2,1) psi <- c(-1,0) k <- length(psi) PSI <- matrix(rep(psi,rep(n,k)),ncol=k) XP <- matrix(rep(X,k),nrow=n) XR <- cbind(1,X,pmax((XP-PSI),0),Z) bet <- c(1,-1,0,0,sqrt(3),-sqrt(3)) Y <- XR %*% bet + epsilon obj <- KinkTest(y=Y,thre.x=X,cont.z=Z, bandwidth_type=c("Hall-Sheather")) obj$pv ## Not run: # Example 2: longitudinal data library(quantreg) N = 200 T = 5 subject = rep(1:N,each=T) NT = N*T Z1 <- rexp(NT,1) Z2 <- rbinom(NT,1,0.5) Z <- cbind(Z1,Z2) epsilon <- rnorm(NT,0,1) X <- runif(NT,-2,1) psi <- c(-1,0) k <- length(psi) PSI <- matrix(rep(psi,rep(NT,k)),ncol=k) a <- rnorm(N,0,1) A <- rep(a,each=T) XP <- matrix(rep(X,k),nrow=NT) XR <- cbind(1,X,pmax((XP-PSI),0),Z) bet <- c(1,-1,0,0,sqrt(3),-sqrt(3)) Y <- XR %*% bet + A + epsilon obj <- KinkTest(y=Y,thre.x=X,cont.z=Z,id=subject, bandwidth_type=c("Hall-Sheather")) obj$pv ## End(Not run) ```

KinkTest function