empcopula.simulate {LLAhclust}R Documentation

Simulation step used in the independence test based on the empirical copula process implemented in the LLAsimvar function

Description

Simulation step used in the independence test based on the empirical copula process as proposed by Christian Genest and Bruno Rémillard. To be used in conjunction with the LLAsimvar function (method="empirical.copula"). The simulation step consists in simulating the distribution of the test statistic under independence for the sample size under consideration. More details can be found in the articles cited in the reference section.

Usage

empcopula.simulate(n, N = 2000)

Arguments

n Sample size when simulating the distribution of the test statistic under independence.
N Number of repetitions when simulating under independence.

Details

See the references below for more details, especially the third one.

Value

The function empcopula.simulate returns an object of class empcop.simulation whose attributes are: sample.size, number.repetitons and dist.independence (a vector of length N containing the values of the test statistic for each each repetition).

References

P. Deheuvels (1979), La fonction de dépendance empirique et ses propriétés: un test non paramétrique d'indépendance, Acad. Roy. Belg. Bull. Cl. Sci. 5th Ser. 65, 274-292.

P. Deheuvels (1981), A non parametric test for independence, Publ. Inst. Statist. Univ. Paris 26, 29-50.

C. Genest and B. Rémillard (2004). Tests of independence and randomness based on the empirical copula process. Test, 13, 335-369.

C. Genest, J.-F. Quessy and B. Rémillard (2006). Local efficiency of a Cramer-von Mises test of independence. Journal of Multivariate Analysis, 97, 274-294.

C. Genest, J.-F. Quessy and B. Rémillard (2007). Asymptotic local efficiency of Cramer-von Mises tests for multivariate independence. The Annals of Statistics, 35, in press.

I. Kojadinovic (2007), Hierarchical clustering of continuous variables based on the empirical copula process, submitted.

See Also

LLAsimvar,
LLAhclust.

Examples

data(USArrests)

## Compute similarities between variables using the test of
## independence a la Deheuvels based on the empirical copula
## process recently studied by Genest and Remillard: 
s <- LLAsimvar(USArrests, method = "empirical.copula")
s

## The previous computation could have been done in two steps:
d <- empcopula.simulate(n=50,N=2000)
s <- LLAsimvar(USArrests, method = "empirical.copula",
                       simulated.distribution = d)
s
  

[Package LLAhclust version 0.2-2 Index]