gofTstat {copula} | R Documentation |
gofTstat()
computes various goodness-of-fit test statistics
typically used in gofCopula(*, simulation = "pb")
.
gofTstat(u, method = c("Sn", "SnB", "SnC", "AnChisq", "AnGamma"), useR = FALSE, ...)
u |
n x d-matrix of values in [0,1], supposedly independent uniform observations in the hypercube, that is, U_i ~ U[0,1]^d, i.i.d., for i in 1..n. |
method |
a
|
useR |
logical indicating whether an R or C implementation is used. |
... |
additional arguments passed for computing the different test statistics. |
This function should be used with care. The different test statistics were implemented (partly) for different purposes and goodness-of-fit tests and should be used only with knowledge about such (see the references for more details).
The value of the test statistic, a numeric
.
Genest, C., Rémillard, B., and Beaudoin, D. (2009), Goodness-of-fit tests for copulas: A review and a power study Insurance: Mathematics and Economics 44, 199–213.
Rosenblatt, M. (1952), Remarks on a Multivariate Transformation, The Annals of Mathematical Statistics 23, 3, 470–472.
Hering, C. and Hofert, M. (2014), Goodness-of-fit tests for Archimedean copulas in high dimensions, Innovations in Quantitative Risk Management.
Hofert, M., Mächler, M., and McNeil, A. J. (2012). Likelihood inference for Archimedean copulas in high dimensions under known margins. Journal of Multivariate Analysis 110, 133–150.
gofCopula()
for goodness-of-fit tests where (some of)
these test statistics are used.
## generate data cop <- archmCopula("Gumbel", param=iTau(gumbelCopula(), 0.5), dim=5) set.seed(1) U <- rCopula(1000, cop) ## compute Sn (as is done in a parametric bootstrap, for example) Uhat <- pobs(U) # pseudo-observations u <- cCopula(Uhat, copula = cop) # Rosenblatt transformed data (with correct copula) gofTstat(u, method = "Sn", copula = cop) # compute test statistic Sn; requires copula argument