Dependence Properties of Conditional Distributions of some Copula Models
- 159 Downloads
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.
KeywordsFactor model Markov tree Mixture of conditional distributions Positive dependence Stochastically increasing Total positivity of order 2 Vine
Unable to display preview. Download preview PDF.
- Barlow RE, Proschan F (1981) Statistical theory of reliability and life testing. To Begin With, Silver Spring, MDGoogle Scholar
- Cooke R, Joe H, Chang B (2015) Vine regression. Technical report, Resources for the Future, RFF DP 15–52Google Scholar
- Kendall M, Stuart A (1977) The advanced theory of statistics, vol 2, 4th edn. Charles Griffin & Co. Ltd., LondonGoogle Scholar
- Kraus D, Czado C (2016) D-vine copula based quantile regression. Technical report, Technische Universität MünchenGoogle Scholar