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Activity Number: 355 - Advanced Bayesian Topics (Part 4)
Type: Contributed
Date/Time: Thursday, August 12, 2021 : 10:00 AM to 11:50 AM
Sponsor: Section on Bayesian Statistical Science
Abstract #319079
Title: Bayesian Composite Non-Crossing Quantile Curves Fitting
Author(s): Zhongheng Cai* and Qiao Wang and Dongchu Sun
Companies: East China Normal University and Department of Statistics, MU; Missouri Cancer Registry and Research Center and University of Nebraska-Lincoln
Keywords: Bayesian analysis; non-crossing quantile curves; pseudo composite asymmetric Laplace likelihood; smoothing spline

Bayesian simultaneous quantile curve fitting suffers from limitations in constructing a proper model and accommodating the non-crossing constraints. We propose two novel Bayesian composite approaches to fit a set of quantiles depending on whether the underlying curves are parallel (BCQSSP) or nonparallel (BCQSSNP). Compared with existing literature, our approaches not only improve the information sharing among different quantile curves but also enable a direct inference for the difference of quantile curves under the non-crossing constraints. For BCQSSP, we first propose the target minimization problem containing two smoothness penalties imposed on the chosen quantile space and predictor space. BCQSSNP further adapts the varying difference among quantile curves via incorporating a smoothing function in the target minimization with B-spline serving as an approximation. Then the corresponding Bayesian solutions and computation algorithms are offered. Our extensive simulation studies and two real data analyses show that our methods outperform in general and more advantages are observed for the extreme quantiles and heavy-tailed random errors.

Authors who are presenting talks have a * after their name.

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