A1853
Title: A general Bayesian approach to multiple-output quantile regression
Authors: Annika Camehl - Erasmus University Rotterdam (Netherlands) [presenting]
Dennis Fok - Erasmus University Rotterdam (The Netherlands)
Kathrin Gruber - Erasmus University Rotterdam (Netherlands)
Abstract: Regression quantiles reveal relationships between variables outside the center of the distribution. Simultaneously studying multiple responses requires multivariate quantiles. Current definitions of multivariate quantiles can cover large parts of the domain with very low probability, and/or their covered probability does not equal the pre-set quantile level. We suggest superlevel sets of the multivariate density function as an alternative multivariate quantile definition. This quantile set contains all points in the domain for which the density exceeds a certain level. We show that such a quantile has a number of favorable mathematical and intuitive features. For empirical applications, we, first, use an overfitting Gaussian mixture model to fit the multivariate density and, next, calculate the multivariate quantile for a conditional or marginal density of interest. Operating on the same estimated density guarantees logically consistent quantiles. In particular, the quantiles are non-crossing. We use simulation to show that we recover the true quantiles for distributions with correlation, heteroskedasticity, or asymmetry in the disturbances, and we apply our method to study heterogeneity in household expenditures.
