Flexible Quantile Contour Estimation for Multivariate Functional Data: Beyond Convexity

• Activity Number: 344 - Student Paper Award and John M. Chambers Statistical Software Award
• Type: Topic-Contributed
• Date/Time: Thursday, August 12, 2021 : 10:00 AM to 11:50 AM
• Sponsor: Section on Statistical Computing
• Author(s): Gaurav Agarwal* and Wei Tu and Ying Sun and Linglong Kong
• Companies: King Abdullah University of Science and Technology and University of Alberta and King Abdullah University of Science and Technology (KAUST) and University of Alberta
• Keywords: Consistency; functional data analysis; multivariate quantile; nonconvex; quantile contour; PM2.5

Abstract

Nowadays, multivariate functional data are frequently observed in many scientific fields, and the estimation of quantiles of these data is essential in data analysis. This article proposes a new method to estimate the quantiles for multivariate functional data with application to air pollution data. The proposed multivariate functional quantile model is a nonparametric, time-varying coefficient model, and basis functions are used for the estimation and prediction. The estimated quantile contours can characterize non-Gaussian and even nonconvex multivariate distributions marginally. Computationally, the proposed method is efficient for high dimensions and can handle more than just bivariate functional data. The monotonicity, uniqueness, and consistency of the estimated multivariate quantile function have been established. The proposed method was applied to study the joint distribution of PM2.5 (particulate matter) and geopotential height over time in the Northeastern United States; the estimated contours highlight the nonconvex joint distribution, and the functional quantile curves capture the dynamic change across time.