CDVineClarkeTest {CDVine} | R Documentation |
This function performs a Clarke test between two d-dimensional C- or D-vine copula models, respectively.
CDVineClarkeTest(data, Model1.order=1:dim(data)[2], Model2.order=1:dim(data)[2], Model1.family, Model2.family, Model1.par, Model2.par, Model1.par2=rep(0,dim(data)[2]*(dim(data)[2]-1)/2), Model2.par2=rep(0,dim(data)[2]*(dim(data)[2]-1)/2), Model1.type, Model2.type)
data |
An N x d data matrix (with uniform margins). |
Model1.order, Model2.order |
Two numeric vectors giving the order of the variables in the first D-vine trees
or of the C-vine root nodes in models 1 and 2
(default: |
Model1.family, Model2.family |
Two d*(d-1)/2 numeric vectors of the pair-copula families of models 1 and 2, respectively, with values |
Model1.par, Model2.par |
Two d*(d-1)/2 numeric vectors of the (first) copula parameters of models 1 and 2, respectively. |
Model1.par2, Model2.par2 |
Two d*(d-1)/2 numeric vectors of the second copula parameters of models 1 and 2, respectively;
necessary for t, BB1, BB6, BB7 and BB8 copulas. If no such families are included in |
Model1.type, Model2.type |
Type of the respective vine model: |
The test proposed by Clarke (2007) allows to compare non-nested models. For this let c_1 and c_2 be two competing vine copulas in terms of their densities and with estimated parameter sets θ_1 and θ_2. The null hypothesis of statistical indistinguishability of the two models is
H_0: P(m_i > 0) = 0.5 forall i=1,..,N,
where m_i:=log[ c_1(u_i|θ_1) / c_2(u_i|θ_2) ] for observations u_i, i=1,...,N.
Since under statistical equivalence of the two models the log likelihood ratios of the single observations are uniformly distributed around zero and in expectation 50\% of the log likelihood ratios greater than zero, the tets statistic
statistic := B = ∑_{i=1}^N 1_{(0,∞)}(m_i),
where 1 is the indicator function, is distributed Binomial with parameters N and p=0.5, and critical values can easily be obtained. Model 1 is interpreted as statistically equivalent to model 2 if B is not significantly different from the expected value np=N/2.
Like AIC and BIC, the Clarke test statistic may be corrected for the number of parameters used in the models. There are two possible corrections; the Akaike and the Schwarz corrections, which correspond to the penalty terms in the AIC and the BIC, respectively.
statistic, statistic.Akaike, statistic.Schwarz |
Test statistics without correction, with Akaike correction and with Schwarz correction. |
p.value, p.value.Akaike, p.value.Schwarz |
P-values of tests without correction, with Akaike correction and with Schwarz correction. |
Jeffrey Dissmann, Ulf Schepsmeier, Eike Brechmann
Clarke, K. A. (2007). A Simple Distribution-Free Test for Nonnested Model Selection. Political Analysis, 15, 347-363.
CDVineVuongTest
, CDVineAIC
, CDVineBIC
## Not run: # load data set data(worldindices) d = dim(worldindices)[2] # select the C-vine families and parameters cvine = CDVineCopSelect(worldindices,c(1:6),type="CVine") # select the D-vine families and parameters dvine = CDVineCopSelect(worldindices,c(1:6),type="DVine") # compare the two models based on the data clarke = CDVineClarkeTest(worldindices,1:d,1:d,cvine$family,dvine$family, cvine$par,dvine$par,cvine$par2,dvine$par2, Model1.type=1,Model2.type=2) clarke$statistic clarke$statistic.Schwarz clarke$p.value clarke$p.value.Schwarz ## End(Not run)