ExtremalDep (version 0.0.3-3)

fit_pclik_extr_mod: Fit extremal dependence models using pairwise composite likelihood

Description

Estimates the parameters of the Husler-Reiss, Extremal-$t$ and Extremal Skew-$t$ models using pairwise composite likelihood, for up to \(4\) dimensional datasets.

Usage

fit_pclik_extr_mod(model, data, parastart, trace)

Arguments

model

A string with the name of the model: "hr", "Extremalt" or "Skewt".

data

A data.frame or matrix obejct with up to \(4\) columns.

parastart

A vector containing the initial parameter values. See Details.

trace

A non-negative integer. If positive, tracing information on the progress of the optimization is produced. See the options of the routine optim in R for details.

Value

Returns the vector of estimated parameters and the value of the pairwise composite log-likelihood.

Details

Data must be marginally on unit Frechet scale.

If model="hr" then the vector of initial values is made of choose(d,2) positive parameters, d=2,3. If model="Extremalt" then the vector of initial values is made of choose(d,2) dependence parameters and a degree of freedom, d=2,3. If model="Skewt" then the vector of initial values is made of choose(d,2) dependence parameters, d shape (or skewness) parameters and a degree of freedom, d=2,3.

In the case of bivariate data the regular likelihood estimation is performed.

References

Beranger, B. and Padoan, S. A. (2015). Extreme dependence models, chapter of the book Extreme Value Modeling and Risk Analysis: Methods and Applications, Chapman Hall/CRC.

Beranger, B., Padoan, S. A. and Sisson, S. A. (2017). Models for extremal dependence derived from skew-symmetric families. Scandinavian Journal of Statistics, 44(1), 21-45.

Examples

# NOT RUN {
## Reproduce the real data analysis from
## Beranger et al. (2016), Section 5.

data(Wind)

## Vector of starting values
p0 <- c(rep(0.5,3),1)

### CLOU CLAY SALL

# }
# NOT RUN {
ext1 <- fit_pclik_extr_mod("Extremalt", CLOU.CLAY.SALL, p0, 2)
est.ext1 <- round(ext1$par,2)
p01 <- c(ext1$par[1:3],rep(0,3),ext1$par[4])
skewt1 <- fit_pclik_extr_mod("Skewt", CLOU.CLAY.SALL, p01, 2)
est.skewt1 <- round(skewt1$par,2)
# }
# NOT RUN {
### CLOU CLAY PAUL

# }
# NOT RUN {
ext2 <- fit_pclik_extr_mod("Extremalt", CLOU.CLAY.PAUL, p0, 2)
est.ext2 <- round(ext2$par,2)
p02 <- c(ext2$par[1:3],rep(0,3),ext2$par[4])
skewt2 <- fit_pclik_extr_mod("Skewt", CLOU.CLAY.PAUL, p02, 2)
est.skewt2 <- round(skewt2$par,2)
# }
# NOT RUN {
### CLAY SALL PAUL

# }
# NOT RUN {
ext3 <- fit_pclik_extr_mod("Extremalt", CLAY.SALL.PAUL, p0, 2)
est.ext3 <- round(ext3$par,2)
p03 <- c(ext3$par[1:3],rep(0,3),ext3$par[4])
skewt3 <- fit_pclik_extr_mod("Skewt", CLAY.SALL.PAUL, p03, 2)
est.skewt3 <- round(skewt3$par,2)
# }
# NOT RUN {
### CLAY SALL PAUL

# }
# NOT RUN {
ext4 <- fit_pclik_extr_mod("Extremalt", CLOU.SALL.PAUL, p0, 2)
est.ext4 <- round(ext4$par,2)
p04 <- c(ext4$par[1:3],rep(0,3),ext4$par[4])
skewt4 <- fit_pclik_extr_mod("Skewt", CLOU.SALL.PAUL, p04, 2)
est.skewt4 <- round(skewt4$par,2)
# }
# NOT RUN {
# }