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Methodology and Computing in Applied Probability

, Volume 20, Issue 3, pp 975–1001 | Cite as

Dependence Properties of Conditional Distributions of some Copula Models

  • Harry Joe
Article

Abstract

For multivariate data from an observational study, inferences of interest can include conditional probabilities or quantiles for one variable given other variables. For statistical modeling, one could fit a parametric multivariate model, such as a vine copula, to the data and then use the model-based conditional distributions for further inference. Some results are derived for properties of conditional distributions under different positive dependence assumptions for some copula-based models. The multivariate version of the stochastically increasing ordering of conditional distributions is introduced for this purpose. Results are explained in the context of multivariate Gaussian distributions, as properties for Gaussian distributions can help to understand the properties of copula extensions based on vines.

Keywords

Factor model Markov tree Mixture of conditional distributions Positive dependence Stochastically increasing Total positivity of order 2 Vine 

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Copyright information

© Springer Science+Business Media New York 2017

Authors and Affiliations

  1. 1.Department of StatisticsUniversity of British ColumbiaVancouverCanada

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