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]