gofOutputHybrid: Output Hybrid gof test
In gofCopula: Goodness-of-Fit Tests for Copulae

Description Usage Arguments Details Value References Examples

gofOutputHybrid outputs the desired Hybrid tests from previous test results from this package for the specified testing size.

1	gofOutputHybrid(result, tests = NULL, nsets = NULL)

`result`	An object of `class` gofCOP.
`tests`	Individual tests which should be used in the hybrid test. Submit a vector containing the position of the individual tests as they appear in the object submitted, e.g. `c(1,4)` for the 1st and 4th tests. If `tests` is set NULL (default), all possible testing sizes are returned.
`nsets`	The desired number of tests to be included in each hybrid test. It should be an integer larger than 1 and smaller or equal than the number of tests given in `result`. If `nsets` is set NULL (default), all possible testing sizes are calculated.

In most of scenarios for goodness-of-fit tests, including the one for copula models (e.g. Genest et al. (2009)) there exists no single dominant optimal test. Zhang et al. (2015) proposed a hybrid test which performed in their simulation study more desirably compared to the applied single tests.

The p-value is a combination of the single tests in the following way:

pn^(hybrid) = min(q x min(pn^(1), ..., pn^(q)), 1)

where q is the number of tests and pn^(i) the p-value of the test i. It is ensured that the hybrid test is consistent as long as at least one of the tests is consistent.

The computation of the individual p-values is performed as described in the details of this tests. Note that the derivation differs.

An object of the class gofCOP with the components

`method`	a character which informs about the performed analysis
`copula`	the copula tested for
`margins`	the method used to estimate the margin distribution.
`param.margins`	the parameters of the estimated margin distributions. Only applicable if the margins were not specified as `"ranks"` or `NULL`.
`theta`	dependence parameters of the copulae
`df`	the degrees of freedem of the copula. Only applicable for t-copula.
`res.tests`	a matrix with the p-values and test statistics of the hybrid and the individual tests

Zhang, S., Okhrin, O., Zhou, Q., and Song, P.. Goodness-of-fit Test For Specification of Semiparametric Copula Dependence Models. Journal of Econometrics, 193, 2016, pp. 215-233 doi: 10.1016/j.jeconom.2016.02.017

data(IndexReturns2D)

res1 = gof(IndexReturns2D, priority = "tests", copula = "normal", 
           tests = c("gofKendallCvM", "gofRosenblattSnC", "gofKendallKS"), 
           M = 5)
gofOutputHybrid(res1, tests = 1, nsets = 2)
# mind the difference to the regular output
res1