selectCopC {CopCTS} | R Documentation |

Among a list of copulas, select the one that gives the estimates closest to the empirical copula function.

```
selectCopC(cop.type=c("Clayton","Gaussian","Gumbel","Joe","Frank"),
Yc,d,delta,nIS=500,jumps=NULL,MARGIN=NULL,...,intervals=NULL)
```

`cop.type` |
a Kx1 vector containing the candidate copulas, where K = length(cop.type) is the number of candidate copulas. There are currently five available copula funcitons, including Clayton copula, Gaussian copula, Gumbel copula, Joe copula and Frank copula. Select each by specifying a vector consisting of at least one element from c("Clayton","Gaussian","Gumbel","Joe","Frank"). |

`Yc` |
the Nx1 vector of observed responses that are subject to lower detection limit. |

`d` |
the lower detection limit. |

`delta` |
the Nx1 vector of censoring indicator with 1 indicating uncensored and 0 indicating left censored. |

`nIS` |
the size for sequential importance sampling. The default is 500. |

`jumps` |
the Nx1 vector indicating whether each time t is a start of a new time series, which is deemed to be independent from the previous series. |

`MARGIN` |
the marginal distribution of the latent time series. |

`...` |
additional parameters for the marginal distribution of the latent time series. |

`intervals` |
a 2xK matrix specifying the lower and upper bound for the copula parameter of each candidate copula, where K is the number of candidate copulas. |

`selectCopC`

returns a list of components including

`paras` |
a Kx1 vector containing the estimated copula parameters for each candidate copula. |

`likelihoods` |
a Kx1 vector containing the negative log-likelihood value corresponding to the estimated copula parameter for each candidate copula. |

`estCop` |
a list containing the estimated copula object for each candidate. |

`L2distance` |
a Kx1 vector containing the L2 distance between each copula with estimated copula parameter and the empirical copula function. |

`Selected` |
The selected copula object. |

Li, F., Tang, Y. and Wang, H. (2018) Copula-based Semiparametric Analysis for Time Series Data with Detection Limits, technical report.

```
### Example with simulated data
set.seed(20)
Y = genLatentY("Clayton",1,30,MARGIN.inv = qt,df=3)
d = -1
Yc = pmax(d,Y)
delta = (Y>d)
selectCopC(cop.type=c("Clayton","Frank"),Yc = Yc,d = d,delta = delta,nIS=50)
### Example with water data
attach(water)
Yc = TNH3[1:30]
delta = Delta[1:30]
jumps = Indep[1:30]
set.seed(1)
intv.Gaussian = c(-1,1)
intv.Clayton = c(0,20)
intv.Frank = c(0,15)
intervals = cbind(intv.Gaussian,intv.Clayton,intv.Frank)
cop.type = c("Gaussian","Clayton","Frank")
selCopC <- selectCopC(cop.type=cop.type,Yc=Yc,d=0.02,
delta=delta,nIS = 50,jumps=jumps,intervals=intervals)
selCopC$Selected
```

[Package *CopCTS* version 1.0.0 Index]