copula (version 0.999-15)

gofTstat: Goodness-of-fit Test Statistics

Description

gofTstat() computes various goodness-of-fit test statistics typically used in gofCopula(*, simulation = "pb").

Usage

gofTstat(u, method = c("Sn", "SnB", "SnC", "AnChisq", "AnGamma"), useR = FALSE, ...)

Arguments

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 character string specifying the goodness-of-fit test statistic to be used, which has to be one (or a unique abbreviation) of

useR

logical indicating whether an R or C implementation is used.

...

additional arguments passed for computing the different test statistics.

Value

The value of the test statistic, a numeric.

Details

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).

References

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.

See Also

gofCopula() for goodness-of-fit tests where (some of) these test statistics are used.

Examples

## 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