PDE-regularised spatial quantile regression

Keywords

Statistics
Statistical learning
Geosciences/Protection of Land and Water Resources
Code:
98/2024
Title:
PDE-regularised spatial quantile regression
Date:
Thursday 14th November 2024
Author(s):
Castiglione, C.; Arnone, E.; Bernardi, M.; Farcomeni, A.; Sangalli, L.M.
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Abstract:
We consider the problem of estimating the conditional quantiles of an unknown distribution from data gathered on a spatial domain. We propose a spatial quantile regression model with differential regularisation. The penalisation involves a partial differential equation defined over the considered spatial domain, that can display a complex geometry. Such regularisation permits, on one hand, to model complex anisotropy and non-stationarity patterns, possibly on the basis of problem-specific knowledge, and, on the other hand, to comply with the complex conformation of the spatial domain. We define an innovative functional Expectation-Maximisation algorithm, to estimate the unknown quantile surface. We moreover describe a suitable discretisation of the estimation problem, and investigate the theoretical properties of the resulting estimator. The performance of the proposed method is assessed by simulation studies, comparing with state-of-the-art techniques for spatial quantile regression. Finally, the considered model is applied to two real data analyses, the first concerning rainfall measurements in Switzerland and the second concerning sea surface conductivity data in the Gulf of Mexico.
This report, or a modified version of it, has been also submitted to, or published on
Journal of Multivariate Analysis (2025), Vol. 205, 105381. https://doi.org/10.1016/j.jmva.2024.105381