ExtremalDep (version 1.0.0)

fExtDep: Extremal Dependence Estimation

Description

Estimate the parameters of extremal dependence models using frequentist, composite likelihood, or Bayesian approaches.

Usage

fExtDep(x, method = "PPP", model, par.start = NULL, 
        c = 0, optim.method = "BFGS", trace = 0,
        Nsim, Nbin = 0, Hpar, MCpar, seed = NULL)
        
# S3 method for ExtDep_Freq
plot(x, type, log = TRUE, contour = TRUE, style, labels, 
                           cex.dat = 1, cex.lab = 1, cex.cont = 1, Q.fix, Q.range, 
                           Q.range0, cond = FALSE, ...)        
        
# S3 method for ExtDep_Freq
logLik(object, ...)
# S3 method for ExtDep_Bayes
plot(x, type, log = TRUE, contour = TRUE, style, labels, 
                            cex.dat = 1, cex.lab = 1, cex.cont = 1, Q.fix, Q.range, 
                            Q.range0, cond = FALSE, cred.ci = TRUE, subsamp, ...)          
                            
# S3 method for ExtDep_Bayes
summary(object, cred = 0.95, plot = FALSE, ...)

Value

fExtDep:

• For "PPP" or "Composite": an object of class ExtDep_Freq with elements

  model

  The fitted model.

  par

  Estimated parameters.

  LL

  Maximized log-likelihood.

  SE

  Standard errors.

  TIC

  Takeuchi Information Criterion.

  data

  Input data.

• For "BayesianPPP": an object of class ExtDep_Bayes with elements

  stored.values

  Posterior sample matrix of size \((Nsim-Nbin) \times d\).

  llh

  Log-likelihoods at posterior samples.

  lprior

  Log-priors at posterior samples.

  arguments

  Algorithm details.

  elapsed

  Elapsed run time.

  Nsim, Nbin

  Simulation settings.

  n.accept, n.accept.kept

  MCMC acceptance counts.

  emp.mean

  Posterior means.

  emp.sd

  Posterior standard deviations.

  BIC

  Bayesian Information Criterion.

logLik: numerical log-likelihood value.

Arguments

x

fExtDep: A matrix containing the data. plot methods: an object returned by fExtDep.

object

For summary.ExtDep_Bayes: an object of class ExtDep_Bayes. For logLik: an object returned by fExtDep.

method

Estimation method: "PPP", "BayesianPPP", or "Composite".

model

Name of the model. For "PPP" or "BayesianPPP": "PB", "HR", "ET", "EST", "TD", "AL". For "Composite": "HR", "ET", or "EST".

par.start

Vector of initial parameter values for optimization.

c

Real in \([0,1]\), required for some models under "PPP" or "BayesianPPP" ("ET", "EST", "AL"). See dExtDep.

optim.method

Optimization algorithm (see optim). Required for "PPP" or "Composite".

trace

Non-negative integer controlling optimization progress output (see optim).

Nsim

Number of MCMC simulations (for "BayesianPPP").

Nbin

Burn-in length (for "BayesianPPP").

Hpar

List of hyper-parameters (see Details). Required for "BayesianPPP".

MCpar

Variance of the proposal distribution (see Details). Required for "BayesianPPP".

seed

Integer seed for reproducibility (passed to set.seed).

type

For plot methods: plot type, one of "angular", "pickands", or "returns".

log

Logical; applies to "angular" and "pickands" plots (see angular.plot, pickands.plot).

contour

Logical; applies to "angular" and "pickands" plots.

style

For "angular" plots: "hist" or "ticks" (default).

labels

Labels for axes in plot methods.

cex.dat

Point size for 3D angular plots.

cex.lab

Label size in plots.

cex.cont

Contour line size in "angular" or "pickands" plots.

Q.fix, Q.range, Q.range0, cond

Arguments for "returns" plots (see returns.plot).

cred.ci

Logical, for "returns" plots under "BayesianPPP"; if TRUE, compute 95% credible bands.

subsamp

Posterior subsample percentage (used with cred.ci=TRUE).

cred

Credible interval coverage probability (default 0.95).

plot

Logical; if TRUE, plot kernel densities of posterior parameters (for summary.ExtDep_Bayes).

...

Additional graphical or density arguments (see Details).

Author

Simone Padoan (, https://faculty.unibocconi.it/simonepadoan/) Boris Beranger (, https://www.borisberanger.com)

Details

Estimation:

• method="PPP": Approximate likelihood estimation using dExtDep(method="Parametric", angular=TRUE).

• method="BayesianPPP": Bayesian estimation of the spectral measure (Sabourin et al., 2013; Sabourin & Naveau, 2014). Requires Hpar and MCpar. Hyper-parameters depend on the model (see references for details).

• method="Composite": Pairwise composite likelihood using dExtDep(method="Parametric", angular=FALSE).

Plotting:

See angular.plot, pickands.plot, and returns.plot. Angular plots can display data as histograms (style="hist") or ticks (style="ticks"). For trivariate cases, use cex.dat to control point size.

References

Beranger, B. and Padoan, S. A. (2015). Extreme Dependence Models, in Extreme Value Modeling and Risk Analysis: Methods and Applications, Chapman & Hall/CRC.

Sabourin, A., Naveau, P., and Fougeres, A.-L. (2013). Bayesian model averaging for multivariate extremes. Extremes, 16, 325-350.

Sabourin, A. and Naveau, P. (2014). Bayesian Dirichlet mixture model for multivariate extremes: A re-parametrization. Computational Statistics & Data Analysis, 71, 542-567.

See Also

dExtDep, pExtDep, rExtDep, fExtDep.np

Examples

# Poisson Point Process approach
data(pollution)
# \donttest{
  f.hr <- fExtDep(x = PNS, method = "PPP", model = "HR", 
                  par.start = rep(0.5, 3), trace = 2)
  plot(f.hr, type = "angular",
       labels = c(expression(PM[10]), expression(NO), expression(SO[2])), 
       cex.lab = 2)
  plot(f.hr, type = "pickands",
       labels = c(expression(PM[10]), expression(NO), expression(SO[2])), 
       cex.lab = 2) # may be slow
# }

# Pairwise composite likelihood
# \donttest{
  set.seed(1)
  data <- rExtDep(n = 300, model = "ET", par = c(0.6, 3))
  f.et <- fExtDep(x = data, method = "Composite", model = "ET", 
                  par.start = c(0.5, 1), trace = 2)
  plot(f.et, type = "angular", cex.lab = 2)                  
# }