Inference and sampling for archimax copulas
AUTHORs: 
Yuting Ng, Ali Hasan, Vahid TarokhAuthors Info & Claims
Article No.: 1244, Pages 17099 - 17116
Abstract
Understanding multivariate dependencies in both the bulk and the tails of a distribution is an important problem for many applications, such as ensuring algorithms are robust to observations that are infrequent but have devastating effects. Archimax copulas are a family of distributions endowed with a precise representation that allows simultaneous modeling of the bulk and the tails of a distribution. Rather than separating the two as is typically done in practice, incorporating additional information from the bulk may improve inference of the tails, where observations are limited. Building on the stochastic representation of Archimax copulas, we develop a non-parametric inference method and sampling algorithm. Our proposed methods, to the best of our knowledge, are the first that allow for highly flexible and scalable inference and sampling algorithms, enabling the increased use of Archimax copulas in practical settings. We experimentally compare to state-of-the-art density modeling techniques, and the results suggest that the proposed method effectively extrapolates to the tails while scaling to higher dimensional data. Our findings suggest that the proposed algorithms can be used in a variety of applications where understanding the interplay between the bulk and the tails of a distribution is necessary, such as healthcare and safety.
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AbstractThe class of Archimax copulas is generalized to hierarchical Archimax copulas in two ways. First, a hierarchical construction of d-norm generators is introduced to construct hierarchical stable tail dependence functions which induce a ...
d-Dimensional dependence functions and Archimax copulas
We introduce a new class of dependence functions and method for constructing tail and Pickands dependence functions. Finally, we conjecture the structure of d-dimensional Archimax copulas and discuss some classes of d-dimensional Archimax copulas.
Extremal dependence of copulas: A tail density approach
The extremal dependence of a random vector describes the tail behaviors of joint probabilities of the random vector with respect to that of its margins, and has been often studied by using the tail dependence function of its copula. A tail density ...
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Published In
November 2022
39114 pages
ISBN:9781713871088
- Editors:
- S. Koyejo,
- S. Mohamed,
- A. Agarwal,
- D. Belgrave,
- K. Cho,
- A. Oh
Copyright © 2022 Neural Information Processing Systems Foundation, Inc.
Publisher
Curran Associates Inc.
Red Hook, NY, United States
Publication History
Published: 03 April 2024
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