New Directions in Quantile-based Modeling and Analysis

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Quantile as a data descriptive and analytic tool has earned its place in statistics for over a hundred years. In recent years, research on quantile modeling to incorporate the effect of covariates and to handle multivariate data has accelerated in response to the needs arising from a broad area of applications. The investigator addresses an important but often neglected question on the validity of posterior inference on quantile regression for the pseudo-Bayesian methods that have become popular in the literature. The investigator conducts a careful investigation into how the choice of a working likelihood and the choice of a prior play their respective roles, both in finite-sample problems, and in the asymptotic theory. The investigator studies a new class of shrinking priors as an asymptotic framework to understand the efficiency gains of the Bayesian methods for estimation and prediction of quantiles in data sparse areas and in problems involving high dimensional covariates. The proposed research will deepen our understanding of the validity of pseudo-posterior inference and suggest asymptotically valid and efficient inferential methods for quantile regression at single or multiple quantile levels. The research will also facilitate a new pseudo-Bayesian framework for model selection beyond quantile regression. Furthermore, the investigator studies a new notion of quantile for multivariate data.The proposed activities will stimulate novel ideas and critical thinking in the areas of quantile modeling and Bayesian inference. The new insights and the new tools to be developed will be useful for estimation, prediction, and hypothesis testing regarding rare events in climate research, public health, and other scientific endeavors. The notion of multivariate quantiles will lead to an efficient statistical downscaling method for better climate projections at localized scales. The proposed activities will engage graduate students directly as part of their academic training. The investigator will work with other researchers and scientists to ensure that the research results are disseminated appropriately to the broad scientific community.