KinkTest {MultiKink}

Test the existence of kink effect in the multi-kink quantile regression

Description

This function tests the existence of a kink effect in the multi-kink quantile regression.

Usage

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").

Value

A list containing the p-value (pv), the statistic based on the original data (Tn), and the statistics by wild bootstrap (Tn.NB).

Examples

# 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)