Test.Clayton {Copula.surv} R Documentation

## A goodness-of-fit test for the Clayton copula

### Description

Perform a goodness-of-fit test for the Clayton copula based on Emura, Lin and Wang (2010). The test is asymptotically equivalent to the test of Shih (1998).

### Usage

```Test.Clayton(x.obs,y.obs,dx,dy,lower=0.001,upper=50,U.plot=TRUE)
```

### Arguments

 `x.obs` censored times for X `y.obs` censored times for Y `dx` censoring indicators for X `dy` censoring indicators for Y `lower` lower bound for the association parameter `upper` upper bound for the association parameter `U.plot` if TRUE, draw the plot of U_1(theta)

### Details

See the references.

### Value

 `alpha1` association parameter by the pseudo-likelihood estimator `alpha2` association parameter by the unweighted estimator `Stat` log(alpha1)-log(alpha2) `Z` Z-value of the goodness-of-fit for the Clayton copula `P` P-value of the goodness-of-fit for the Clayton copula

Takeshi Emura

### References

Emura T, Lin CW, Wang W (2010) A goodness-of-fit test for Archimedean copula models in the presence of right censoring, Compt Stat Data Anal 54: 3033-43

Shih JH (1998) A goodness-of-fit test for association in a bivariate survival model. Biometrika 85: 189-200

### Examples

```n=20
set.seed(1)
Dat=simu.Clayton(n=n,alpha=2)
C=runif(n,min=0,max=5)
x.obs=pmin(Dat[,"X"],C)
y.obs=pmin(Dat[,"Y"],C)
dx=Dat[,"X"]<=C
dy=Dat[,"Y"]<=C
Test.Clayton(x.obs,y.obs,dx,dy)
```

[Package Copula.surv version 1.1 Index]