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Clayton_Frank_Gumbel_and_Gaussian_n=200.R
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Clayton_Frank_Gumbel_and_Gaussian_n=200.R
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#########################################################################
# R functions for testing independence versus positive quadrant #
# dependence corresponding to the manuscript titled, #
# "Testing for positive quadrant dependence." #
# Date: 06/17/2018 #
#########################################################################
library(Rcpp)
library(copula)
source("https://raw.githubusercontent.com/cftang9/PQD/master/EL_PQD_Library.R")
#########################################################################
# Generating critical values for EL, KS, CvM, AD, Spearman, and Kendall
# tests for independence versus PQD from uniform (0,1)^2 with sample
# size n and 10000 Monte Carlo replications.
# (It may take some time to generate critical for large sample sizes,
# for example, 100.)
set.seed(200)
n = 200; #sample size;
alpha = 0.05; #significance level
CV = array(0,6); TestStats = array(,c(10000,6));
for(b in 1:10000){
X0 = array(runif(2*n),c(n,2));
TestStats[b,1] = Rcpp_IP_FF(X0,n);
TestStats[b,2:4] = Rcpp_KCA_01(X0,n);
TestStats[b,5] = cor(X0,method="spearman")[2]
TestStats[b,6] = cor(X0,method="kendall")[2]
}
CV = apply(TestStats,2,quantile,prob=0.95)
CV = data.frame(t(CV))
colnames(CV) = c("EL","KS","CvM","AD","spearman","kendall")
#########################################################################
# Perform simulation using Clayton copula
# with sample size n and B Monte Carlo replications.
B = 10000; #number of Monte Carlo replications
Tau = seq(0,0.4,by=0.1); nTau = length(Tau);
Power = array(0,c(6,nTau));
set.seed(1200)
for(i in 1:nTau){
for(b in 1:B){
if(Tau[i]==0){X = array(runif(2*n),c(n,2)); }
if(Tau[i]> 0){X = RV_CopTau(n, Tau[i], Copula="Clayton"); }
Power[1,i] = c(Rcpp_IP_FF(X,n)>CV[1])/B + Power[1,i];
temp = Rcpp_KCA_01(X,n);
Power[2,i] = c(temp[1]>CV[2])/B + Power[2,i];
Power[3,i] = c(temp[2]>CV[3])/B + Power[3,i];
Power[4,i] = c(temp[3]>CV[4])/B + Power[4,i];
Power[5,i] = c(cor(X,method="spearman")[2]>CV[5])/B + Power[5,i]
Power[6,i] = c(cor(X,method="kendall")[2]>CV[6])/B + Power[6,i]
}
}
colnames(Power) = Tau; rownames(Power) = c("EL","KS","CvM","AD","spearman_rho","kendall_tau")
Power_Clayton = Power;
#########################################################################
# Perform simulation using Frank copula
# with sample size n and B Monte Carlo replications.
B = 10000; #number of Monte Carlo replications
Tau = seq(0,0.4,by=0.1); nTau = length(Tau);
Power = array(0,c(6,nTau));
set.seed(300)
for(i in 1:nTau){
for(b in 1:B){
if(Tau[i]==0){X = array(runif(2*n),c(n,2)); }
if(Tau[i]> 0){X = RV_CopTau(n, Tau[i], Copula="Frank"); }
Power[1,i] = c(Rcpp_IP_FF(X,n)>CV[1])/B + Power[1,i];
temp = Rcpp_KCA_01(X,n);
Power[2,i] = c(temp[1]>CV[2])/B + Power[2,i];
Power[3,i] = c(temp[2]>CV[3])/B + Power[3,i];
Power[4,i] = c(temp[3]>CV[4])/B + Power[4,i];
Power[5,i] = c(cor(X,method="spearman")[2]>CV[5])/B + Power[5,i]
Power[6,i] = c(cor(X,method="kendall")[2]>CV[6])/B + Power[6,i]
}
}
colnames(Power) = Tau; rownames(Power) = c("EL","KS","CvM","AD","spearman_rho","kendall_tau")
Power_Frank = Power
#########################################################################
# Perform simulation using Gumbel copula
# with sample size n and B Monte Carlo replications.
B = 10000; #number of Monte Carlo replications
Tau = seq(0,0.4,by=0.1); nTau = length(Tau);
Power = array(0,c(6,nTau));
set.seed(400)
for(i in 1:nTau){
for(b in 1:B){
if(Tau[i]==0){X = array(runif(2*n),c(n,2)); }
if(Tau[i]> 0){X = RV_CopTau(n, Tau[i], Copula="Gumbel"); }
Power[1,i] = c(Rcpp_IP_FF(X,n)>CV[1])/B + Power[1,i];
temp = Rcpp_KCA_01(X,n);
Power[2,i] = c(temp[1]>CV[2])/B + Power[2,i];
Power[3,i] = c(temp[2]>CV[3])/B + Power[3,i];
Power[4,i] = c(temp[3]>CV[4])/B + Power[4,i];
Power[5,i] = c(cor(X,method="spearman")[2]>CV[5])/B + Power[5,i]
Power[6,i] = c(cor(X,method="kendall")[2]>CV[6])/B + Power[6,i]
}
}
colnames(Power) = Tau; rownames(Power) = c("EL","KS","CvM","AD","spearman_rho","kendall_tau")
Power_Gumbel = Power;
#########################################################################
# Perform simulation using Gaussian copula
# with sample size n and B Monte Carlo replications.
B = 10000; #number of Monte Carlo replications
Rho = seq(0,0.4,by=0.1); nRho = length(Rho);
Power = array(0,c(6,nRho));
set.seed(500)
for(i in 1:nRho){
for(b in 1:B){
if(Rho[i]==0){X = array(runif(2*n),c(n,2)); }
if(Rho[i]> 0){X = RV_CopGaussian(n,Rho[i]) }
Power[1,i] = c(Rcpp_IP_FF(X,n)>CV[1])/B + Power[1,i];
temp = Rcpp_KCA_01(X,n);
Power[2,i] = c(temp[1]>CV[2])/B + Power[2,i];
Power[3,i] = c(temp[2]>CV[3])/B + Power[3,i];
Power[4,i] = c(temp[3]>CV[4])/B + Power[4,i];
Power[5,i] = c(cor(X,method="spearman")[2]>CV[5])/B + Power[5,i]
Power[6,i] = c(cor(X,method="kendall")[2]>CV[6])/B + Power[6,i]
}
}
colnames(Power) = Tau; rownames(Power) = c("EL","KS","CvM","AD","spearman_rho","kendall_tau")
Power_Gaussian = Power;
print("Clayton"); print(Power_Clayton,digit=3);
print("Frank"); print(Power_Frank,digit=3);
print("Gumbel"); print(Power_Gumbel,digit=3);
print("Gaussian"); print(Power_Gaussian,digit=3);