# TwoCop: Nonparametric test of equality between two copulas In TwoCop: Nonparametric test of equality between two copulas

## Description

This function performs the nonparametric test of equality between two copulas proposed by Remillard and Scaillet (2009). The test is based on the Cramer-von-Mises statistic between the two empirical copulas. An approximate p-value is returned.

## Usage

 `1` ```TwoCop(x, y, Nsim=100, paired=FALSE, alpha=0.95) ```

## Arguments

 `x` `n` by `d` matrix containing the first dataset. `y` `m` by `d` matrix containing the second dataset. `Nsim` Number of iterations used in the approximation of the p-value. `paired` `FALSE` (default) means that x and y are from two independent populations, `TRUE` indicates paired data. `alpha` Level of the calculated VaR. Default is 0.95.

## Details

Details of the method can be found in Remillard and Scaillet (2009).

## Value

A list of the following objects:

 `cvm` Value of the Cramer-von Mises test statistic. `pvalue` pvalue based on the multiplier Monte Carlo method with `Nsim` iterations. `cvmsim` Simulated values of the Cramer-von Mises statistic. `VaR` `alpha` quantile of the simulated Cramer-von Mises statistics.

## Author(s)

Bruno Remillard and Jean-Francois Plante

## References

Remillard, B. & Scaillet, O. (2009) Testing for equality between two copulas. Journal of Multivariate Analysis, 100, 377-386.

## Examples

 ``` 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15``` ```# Simulating a bivariate normal (copula = independence) X=matrix(rnorm(100),ncol=2) # Simulating a bivriate exponential distribution with a Clayton copula v=runif(50) theta=1 x<-1/(1/runif(50)/v^(theta+1))^(1/(theta+1)) u<-(x^(-theta)-v^(-theta)+1)^(-1/theta) Y=cbind(-log(1-u),-log(1-v)) # Testing equality of the copulas TwoCop(X,Y)\$pvalue ```

TwoCop documentation built on May 30, 2017, 4:37 a.m.