Estimating an Extreme Bayesian Network via Scalings

12/09/2019
by   Claudia Klüppelberg, et al.
0

Recursive max-linear vectors model causal dependence between its components by expressing each node variable as a max-linear function of its parental nodes in a directed acyclic graph and some exogenous innovation. Motivated by extreme value theory, innovations are assumed to have regularly varying distribution tails. We propose a scaling technique in order to determine a causal order of the node variables. All dependence parameters are then estimated from the estimated scalings. Furthermore, we prove asymptotic normality of the estimated scalings and dependence parameters based on asymptotic normality of the empirical spectral measure. Finally, we apply our structure learning and estimation algorithm to financial data and food dietary interview data.

READ FULL TEXT
research
02/29/2020

Recursive max-linear models with propagating noise

Recursive max-linear vectors model causal dependence between node variab...
research
06/27/2023

Heavy-tailed max-linear structural equation models in networks with hidden nodes

Recursive max-linear vectors provide models for the causal dependence be...
research
03/30/2019

Strong Consistency of Nonparametric Bayesian Inferential Methods for Multivariate Max-Stable Distributions

Predicting extreme events is important in many applications in risk anal...
research
09/29/2022

Max-linear graphical models with heavy-tailed factors on trees of transitive tournaments

Graphical models with heavy-tailed factors can be used to model extremal...
research
01/26/2020

Inference on extremal dependence in a latent Markov tree model attracted to a Hüsler-Reiss distribution

A Markov tree is a probabilistic graphical model for a random vector by ...
research
05/26/2023

An asymptotic expansion of the empirical angular measure for bivariate extremal dependence

The angular measure on the unit sphere characterizes the first-order dep...
research
07/06/2022

Estimating the limiting shape of bivariate scaled sample clouds for self-consistent inference of extremal dependence properties

An integral part of carrying out statistical analysis for bivariate extr...

Please sign up or login with your details

Forgot password? Click here to reset