empcopula.simulate {LLAhclust} | R Documentation |
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.
empcopula.simulate(n, N = 2000)
n |
Sample size when simulating the distribution of the test statistic under independence. |
N |
Number of repetitions when simulating under independence. |
See the references below for more details, especially the third one.
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).
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.
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