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 (n x d) matrix of angular components, where the rows represent n independent points in the d-dimensional unit simplex. |
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 [0,1], providing the decision rule to allocate a data point to a subset of the simplex. Only required for the Extremal-t, Extremal Skew-t and Asymmetric Logistic models. |
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, http://faculty.unibocconi.it/simonepadoan; Boris Beranger, borisberanger@gmail.com http://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) 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) 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) 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) 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)