Integrated Variance Correlation

Description

This function is used to calculate the integrated variance correlation between two random variables or between a random variable and a multivariate random variable

Usage

IVC(y, x, K, NN = 3, type)

Arguments

Value

The value of the corresponding sample statistic

Examples

# linear model
n=100
x=rnorm(n)
y=3*x+rnorm(n)

IVC(y,x,K=5,type="linear")
# nonlinear model
n=100
p=3
x=matrix(NA,nrow=n,ncol=p)
for(i in 1:p){
 x[,i]=rnorm(n)
}
y=cos(x[,1]+x[,2])+x[,3]^2+rnorm(n)
IVC(y,x,K=5,type="nonlinear")

Integrated Variance Correlation with Discrete Response Variable

Description

This function is used to calculate the integrated variance correlation between a discrete response variable and a continuous random variable

Usage

IVCCA(y, x, K)

Arguments

Value

The value of the corresponding sample statistic

Examples

n=100
y=sample(rep(1:3), n, replace = TRUE, prob = c(1/3,1/3,1/3))
x=c()
for(i in 1:n){
 x[i]=rnorm(1,mean=2*y[i],sd=1)
}

IVCCA(y,x,K=5)

Integrated Variance Correlation Based Hypothesis Test for Discrete Response

Description

This function is used to test independence between a categorical variable and a continuous variable using integrated variance correlation

Usage

IVCCAT(y, x, K, num_per, type)

Arguments

Value

The p-value of the corresponding hypothesis test

Examples

# small R
n=100
x=runif(n,0,1)
y=sample(rep(1:3), n, replace = TRUE, prob = c(1/3,1/3,1/3))

IVCCAT(y,x,K=5,num_per=20,type = "fixed")
# large R
n=200
y=sample(rep(1:20), n, replace = TRUE, prob = rep(1/20,20))
mu_x=sample(c(1,2,3,4),20,replace = TRUE,prob = c(1/4,1/4,1/4,1/4))
x=c()
for (i in 1:n) {
 x[i]=2*mu_x[y[i]]+rcauchy(1)
}

IVCCAT(y,x,K=10,type = "infinity")

Critical Values for Integrated Variance Correlation Based Hypothesis Test with Discrete Response

Description

This function is used to calculate the critical values for integrated variance correlation test with discrete response at significance level 0.1, 0.05 and 0.01

Usage

IVCCA_crit(R, N = 500, realizations)

Arguments

Value

The critical values at significance level 0.1, 0.05 and 0.01

Examples

IVCCA_crit(R=5,N=500,realizations=100)

Integrated Variance Correlation with Local Linear Estimation

Description

This function is used to calculate the integrated variance correlation between two random variables with local linear estimation

Usage

IVCLLQ(y, x, K)

Arguments

Value

The value of the corresponding sample statistic

Examples

n=100
x=rnorm(n)
y=exp(x)+rnorm(n)

IVCLLQ(y,x,K=4)

Integrated Variance Correlation Based Hypothesis Test

Description

This function is used to test significance of linear or nonlinear correlation using integrated variance correlation

Usage

IVCT(y, x, K, num_per, NN = 3, type)

Arguments

Value

The p-value of the corresponding hypothesis test

Examples

# linear model
n=100
x=rnorm(n)
y=rnorm(n)

IVCT(y,x,K=5,num_per=20,type = "linear")
# nonlinear model
n=100
p=4
x=matrix(NA,nrow=n,ncol=p)
for(i in 1:p){
 x[,i]=runif(n,0,1)
}
y=3*ifelse(x[,1]>0.5,1,0)*x[,2]+3*cos(x[,3])^2*x[,1]+3*(x[,4]^2-1)*x[,1]+rnorm(n)

IVCT(y,x,K=5,num_per=20,type = "nonlinear")

Integrated Variance Correlation Based Hypothesis Test with Local Linear Estimation

Description

This function is used to test significance using integrated variance correlation with local linear estimation

Usage

IVCTLLQ(y, x, K, num_per)

Arguments

Value

The p-value of the corresponding hypothesis test

Examples

n=100
x=runif(n,-1,1)
y=2*cos(2*x)+rnorm(n)


IVCTLLQ(y,x,K=5,num_per=100)

Integrated Variance Correlation Based Interval Independence Hypothesis Test

Description

This function is used to test interval independence using integrated variance correlation

Usage

IVCT_Interval(y, x, tau1, tau2, K, num_per, NN = 3, type)

Arguments

Value

The p-value of the corresponding hypothesis test

Examples

require("mvtnorm")
n=100
p=3
pho1=0.5
mean_x=rep(0,p)
sigma_x=matrix(NA,nrow = p,ncol = p)
for (i in 1:p) {
 for (j in 1:p) {
   sigma_x[i,j]=pho1^(abs(i-j))
 }
}
x=rmvnorm(n, mean = mean_x, sigma = sigma_x,method = "chol")
y=rnorm(n)

IVCT_Interval(y,x,tau1=0.5,tau2=0.75,K=5,num_per=20,type = "linear")

n=100
x_til=runif(n,min=-1,max=1)
y_til=rnorm(n)
epsilon=rnorm(n)
x=x_til+2*epsilon*ifelse(x_til<=-0.5&y_til<=-0.675,1,0)
y=y_til+2*epsilon*ifelse(x_til<=-0.5&y_til<=-0.675,1,0)

IVCT_Interval(y,x,tau1=0.6,tau2=0.8,K=5,num_per=20,type = "nonlinear")

Integrated Variance Correlation for Interval Independence

Description

This function is used to calculate the integrated variance correlation to measure interval independence

Usage

IVC_Interval(y, x, K, tau1, tau2, NN = 3, type)

Arguments

Value

The value of the corresponding sample statistic for interval independence

Examples

# linear model
require("mvtnorm")
n=100
p=3
pho1=0.5
mean_x=rep(0,p)
sigma_x=matrix(NA,nrow = p,ncol = p)
for (i in 1:p) {
 for (j in 1:p) {
   sigma_x[i,j]=pho1^(abs(i-j))
 }
}
x=rmvnorm(n, mean = mean_x, sigma = sigma_x,method = "chol")
y=2*(x[,1]+x[,2]+x[,3])+rnorm(n)

IVC_Interval(y,x,K=5,tau1=0.4,tau2=0.6,type="linear")
# nonlinear model
n=100
x=runif(n,min=-2,max=2)
y=exp(x^2)*rnorm(n)

IVC_Interval(y,x,K=5,tau1=0.4,tau2=0.6,type="nonlinear")

Critical Values for Integrated Variance Correlation Based Hypothesis Test

Description

This function is used to calculate the critical values for integrated variance correlation test at significance level 0.1, 0.05 and 0.01

Usage

IVC_crit(N = 500, realizations)

Arguments

Value

The critical values at significance level 0.1, 0.05 and 0.01

Examples

IVC_crit(N=500,realizations=100)