# High-Dimensional Spatial Quantile Function-on-Scalar Regression

arXiv: https://arxiv.org/abs/2012.10579 · HTML: https://mlsanity.com/paper/2012.10579/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 19 Dec 2020.

## Built on by (most cited first, 4 of 4)

- [Evaluating Dynamic Conditional Quantile Treatment Effects with Applications in Ridesharing](https://mlsanity.com/paper/2305.10187/) (2023)
- [Interpretable Causal Inference for Analyzing Wearable, Sensor, and Distributional Data](https://mlsanity.com/paper/2312.10569/) (2023)
- [Functional BART with Shape Priors: A Bayesian Tree Approach to Constrained Functional Regression](https://mlsanity.com/paper/2502.16888/) (2025)
- [Partition-Based Functional Ridge Regression for High-Dimensional Data](https://mlsanity.com/paper/2603.11113/) (2026)

## Abstract (arXiv)

This paper develops a novel spatial quantile function-on-scalar regression model, which studies the conditional spatial distribution of a high-dimensional functional response given scalar predictors. With the strength of both quantile regression and copula modeling, we are able to explicitly characterize the conditional distribution of the functional or image response on the whole spatial domain. Our method provides a comprehensive understanding of the effect of scalar covariates on functional responses across different quantile levels and also gives a practical way to generate new images for given covariate values. Theoretically, we establish the minimax rates of convergence for estimating coefficient functions under both fixed and random designs. We further develop an efficient primal-dual algorithm to handle high-dimensional image data. Simulations and real data analysis are conducted to examine the finite-sample performance.