fit_pclik_extr_mod {ExtremalDep} | R Documentation |
Estimates the parameters of the Husler-Reiss, Extremal-$t$ and Extremal Skew-$t$ models using pairwise composite likelihood, for up to 4 dimensional datasets.
fit_pclik_extr_mod(model, data, parastart, trace)
model |
A string with the name of the model: |
data |
A |
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. |
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.
Returns the vector of estimated parameters and the value of the pairwise composite log-likelihood.
Simone Padoan, simone.padoan@unibocconi.it, http://faculty.unibocconi.it/simonepadoan; Boris Beranger, borisberanger@gmail.com http://www.borisberanger.com;
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.
## 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 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) ### CLOU CLAY PAUL 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) ### CLAY SALL PAUL 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) ### CLAY SALL PAUL 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)