alik {ExtremalDep} | R Documentation |
Estimates the parameters of extremal dependence models. It also provides standard errors and TIC.
alik(data, model, parastart, c=NULL, trace=0, sig=3)
data |
A ( |
model |
A string with the name of the parametric model to be estimated. See Details. |
parastart |
A vector containing the starting values of the model's parameters for the maximisation of the log-approximate likelihood. See Details. |
c |
A real value in |
trace |
Non-negative integer. See the options of the routine optim in R for details. |
sig |
Non-negative integer. Provides the number of decimal places for the returned object.
|
The available parametric extremal dependence models are:
The Pairwise Beta, called with model="Pairwise"
. The number of parameters is
choose(d,2)+1
;
The Husler-Reiss, called with model="Husler"
. The number of parameters is
choose(d,2)
;
The Tilted Dirichlet, called with model="Dirichlet"
. The number of parameters is
d
;
The Extremal-t, called with model="Extremalt"
. The number of parameters is choose(d,2)+1
;
The Extremal Skew-t, called with model="Skewt"
. The number of parameters is choose(d,2)+d+1
;
The Asymmetric Logistic, that can be called with model="Asymmetric"
. The number of dependence parameters is 2^{d-1}(d+2)-(2d+1)
.
See References and the references therein.
Standard errors are calculated using the sandwich (Godambe) information matrix.
Returns a list where par
are the estimated parameters, LL
is the value of the maximized
log-likelihood, TIC
is the Takeuchi Information Criterion and SE
are the standard errors.
Simone Padoan, simone.padoan@unibocconi.it, https://mypage.unibocconi.it/simonepadoan/; Boris Beranger, borisberanger@gmail.com https://www.borisberanger.com/;
Beranger, B. and Padoan, S. A. (2015). Extreme dependence models, chapater 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.
################################################
# The following examples provide the fitting
# results of the air quality data recorded in
# the city center of Leeds, UK, analysed in
# Beranger and Padoan (2015).
################################################
## Load datsets
data(pollution)
## Dataset PM10-NO-SO2 (PNS)
if (interactive()){
alik(PNS,model="Pairwise",c(1,1,1,1),trace=2,sig=2)
alik(PNS,model="Husler",rep(1,3),trace=2,sig=2)
alik(PNS,model="Dirichlet",rep(0.1,3),trace=2,sig=2)
alik(PNS,model="Extremalt",c(-0.5,-0.4,-0.5,1),c=0.01,trace=2,sig=2)
alik(PNS,model="Asymmetric",c(rep(1.1,4),rep(0.1,9)),c=0.01,trace=2,sig=2)
}
## Dataset NO2-SO2-NO (NSN)
if (interactive()){
alik(NSN,model="Pairwise",c(1,1,1,1),trace=2,sig=2)
alik(NSN,model="Husler",rep(1,3),trace=2,sig=2)
alik(NSN,model="Dirichlet",rep(0.1,3),trace=2,sig=2)
alik(NSN,model="Extremalt",c(-0.5,-0.4,-0.5,1),c=0.01,trace=2,sig=2)
alik(NSN,model="Asymmetric",c(rep(1.1,4),rep(0.1,9)),c=0.01,trace=2,sig=2)
}
## Dataset PM10-NO-NO2 (PNN)
if (interactive()){
alik(PNN,model="Pairwise",c(1,1,1,1),trace=2,sig=2)
alik(PNN,model="Husler",rep(1,3),trace=2,sig=2)
alik(PNN,model="Dirichlet",rep(0.1,3),trace=2,sig=2)
alik(PNN,model="Extremalt",c(-0.5,-0.4,-0.5,1),c=0.01,trace=2,sig=2)
alik(PNN,model="Asymmetric",c(rep(1.1,4),rep(0.1,9)),c=0.01,trace=2,sig=2)
}
## Dataset PM10-NO-NO2-SO2 (PNNS)
if (interactive()){
alik(PNNS,model="Pairwise",rep(1,choose(ncol(PNNS),2)+1),trace=2,sig=2)
alik(PNNS,model="Husler",rep(1,choose(ncol(PNNS),2)),trace=2,sig=2)
alik(PNNS,model="Dirichlet",rep(1,ncol(PNNS)),trace=2,sig=2)
}