gremes-package: gremes: Estimation of extremal dependence parameters on...

In gremes: Estimation of Tail Dependence in Graphical Models

gremes: Estimation of extremal dependence parameters on graphical models related to trees and block graphs

Description

The package gremes provides tools for estimation of the tail dependence parameters in graphical models parameterized by family of Huesler-Reiss distributions.

Details

The only supported parameterization is through Huesler-Reiss distributions.

The only supported graphs are trees and block graphs.

The estimation methods are variations of method of moments, maximum likelihood and a method based on extremal coefficients.

Estimation methods are based mainly on the following literature:

Asenova, Stefka, Gildas Mazo, and Johan Segers. 2021. "Inference on Extremal Dependence in the Domain of Attraction of a Structured Huesler-Reiss Distribution Motivated by a Markov Tree with Latent Variables." Extremes. https://doi.org/10.1007/s10687-021-00407-5.

Einmahl, J., A. Kiriliouk, and J. Segers. 2017. "A Continuous Updating Weighted Least Squares Estimator of Tail Dependence in High Dimensions." Extremes.

Engelke S. and Hitz A.S. 2020. "Graphical models for extremes" (with discussion). Journal of the Royal Statistical Society: Series B, 82: 871-932.

Vignette "Introduction"

Describes the model, the edge weights that represent the scope of the estimation and how they characterize the tail dependence structure of the model.

Vignette "Detailed contents"

A detailed guide into the documentation of the package and a summary of the main functionalities of the package.

Vignette "Huesler-Reiss distributions"

Parameterizations used of the Huesler-Reiss distributions.

Vignette "Estimation - Note" 1-6

Detailed description of the estimation methods.

Vignettes "Code - Note" 1-6

Use of the estimation tools (the methods, classes and functions) of the package.

Vignette "Additional functionalities"

Explanation and illustrates the functions related to additional functionalities such as generating random sample from a model, computing extremal coefficients, tail dependence coefficients, confidence intervals for one of the estimators.

Object oriented style

The package is developed in an object-oriented style. There are two main types of objects.

An object containing the graph and the dataset is created using classes Network, Tree and possibly other subclasses of these.

An object containing the graph and the edge weights is created with classes HRMnetwork, HRMtree, HRMBG and possibly subclasses of these.

We can look at the first type of objects as one representing the non-parametric view on the problem - all we know is the graph and the data.

We can look at the second type of objects as representing the Huesler-Reiss parametric model: every clique is parameterized by a Huesler-Reiss distribution with parameters - the edge weights within this clique. Hence all that characterizes the parametric model is the graph and the edge weights.

Consider for instance a method extrCoeff which is written both for classes Tree and HRMtree. If we pass an object of class Tree to the method extrCoeff the command will return non-parametric estimates of the extremal coefficients. If the object passed is of class HRMtree the command will return parametric extremal coefficients.

The method estimate

The main goal of the package is estimation, therefore the method estimate is the key functionality of the tools provided in the package. Estimation in gremes happens by using the method estimate on an object from one of the following classes:

MME, MLE1, MLE2, EKS, EKS_part, EngHitz, MMEave, MLEave in which case it estimates the edge weights of a graphical model on a tree. See Vignettes "Code - Node" 1-4 and 6.

HRMBG in which case it estimates the edge weights of a graphical model on a tree. See Vignettes "Code - Node 5".

Author(s)

Stefka Asenova, contact: stefkakirilova at yahoo.com, see also www.gremes.info

gremes documentation built on Feb. 16, 2023, 8:06 p.m.