Fused Adaptive Lasso for Spatial and Temporal Quantile Function Estimation

Abstract

Quantile functions are important in characterizing the entire probability distribution of a random variable, especially when the tail of a skewed distribution is of interest. This article introduces new quantile function estimators for spatial and temporal data with a fused adaptive Lasso penalty to accommodate the dependence in space and time. This method penalizes the difference among neighboring quantiles, hence it is desirable for applications with features ordered in time or space without replicated observations. The theoretical properties are investigated and the performances of the proposed methods are evaluated by simulations. The proposed method is applied to particulate matter (PM) data from the Community Multiscale Air Quality (CMAQ) model to characterize the upper quantiles, which are crucial for studying spatial association between PM concentrations and adverse human health effects.

• Fused adaptive Lasso
• Particulate matter
• Quantile estimation
• Spatial quantiles
• Temporal quantiles

Acknowledgments

The authors thank the valuable suggestions from the associate editor and referees for contributing to the noticeable improvement of the article. This research was partially supported by the US National Science Foundation (NSF) grants DMS-1106862, 1106974, and 1107046, the NSF CAREER award DMS-1149355, and the STATMOS research network on Statistical Methods in Oceanic and Atmospheric Sciences.