Robust quantile estimation and prediction for spatial processes

TL;DR

This paper develops a statistical framework for estimating and predicting conditional quantiles in spatial processes, demonstrating consistency and asymptotic normality of estimators, and illustrating the approach with simulations.

Contribution

It introduces a novel nonparametric method for quantile estimation in spatial processes with strong mixing conditions, including theoretical guarantees.

Findings

Kernel conditional quantile estimator is consistent and asymptotically normal.

The proposed spatial predictor performs well in simulations.

The framework applies to strongly mixing spatial processes.

Abstract

In this paper, we present a statistical framework for modeling conditional quantiles of spatial processes assumed to be strongly mixing in space. We establish the $L_1$ consistency and the asymptotic normality of the kernel conditional quantile estimator in the case of random fields. We also define a nonparametric spatial predictor and illustrate the methodology used with some simulations.