1,242 research outputs found
Extremal attractors of Liouville copulas
Liouville copulas, which were introduced in McNeil and Neslehova (2010), are
asymmetric generalizations of the ubiquitous Archimedean copula class. They are
the dependence structures of scale mixtures of Dirichlet distributions, also
called Liouville distributions. In this paper, the limiting extreme-value
copulas of Liouville copulas and of their survival counterparts are derived.
The limiting max-stable models, termed here the scaled extremal Dirichlet, are
new and encompass several existing classes of multivariate max-stable
distributions, including the logistic, negative logistic and extremal
Dirichlet. As shown herein, the stable tail dependence function and angular
density of the scaled extremal Dirichlet model have a tractable form, which in
turn leads to a simple de Haan representation. The latter is used to design
efficient algorithms for unconditional simulation based on the work of Dombry,
Engelke and Oesting (2015) and to derive tractable formulas for
maximum-likelihood inference. The scaled extremal Dirichlet model is
illustrated on river flow data of the river Isar in southern Germany.Comment: 30 pages including supplementary material, 6 figure
A Bayesian view of doubly robust causal inference
In causal inference confounding may be controlled either through regression
adjustment in an outcome model, or through propensity score adjustment or
inverse probability of treatment weighting, or both. The latter approaches,
which are based on modelling of the treatment assignment mechanism and their
doubly robust extensions have been difficult to motivate using formal Bayesian
arguments, in principle, for likelihood-based inferences, the treatment
assignment model can play no part in inferences concerning the expected
outcomes if the models are assumed to be correctly specified. On the other
hand, forcing dependency between the outcome and treatment assignment models by
allowing the former to be misspecified results in loss of the balancing
property of the propensity scores and the loss of any double robustness. In
this paper, we explain in the framework of misspecified models why doubly
robust inferences cannot arise from purely likelihood-based arguments, and
demonstrate this through simulations. As an alternative to Bayesian propensity
score analysis, we propose a Bayesian posterior predictive approach for
constructing doubly robust estimation procedures. Our approach appropriately
decouples the outcome and treatment assignment models by incorporating the
inverse treatment assignment probabilities in Bayesian causal inferences as
importance sampling weights in Monte Carlo integration.Comment: Author's original version. 21 pages, including supplementary materia
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