Sufficient dimension reduction for regression with spatially correlated errors: application to prediction

TL;DR

This paper develops a method combining sufficient dimension reduction with spatial models to improve prediction accuracy in high-dimensional, spatially correlated data, validated through simulations and real data examples.

Contribution

It introduces a novel integration of SDR with spatial covariance and autoregressive models for better spatial data prediction.

Findings

Effective dimension reduction in spatial data.

Improved prediction accuracy demonstrated.

Method validated with real and simulated data.

Abstract

In this paper, we address the problem of predicting a response variable in the context of both, spatially correlated and high-dimensional data. To reduce the dimensionality of the predictor variables, we apply the sufficient dimension reduction (SDR) paradigm, which reduces the predictor space while retaining relevant information about the response. To achieve this, we impose two different spatial models on the inverse regression: the separable spatial covariance model (SSCM) and the spatial autoregressive error model (SEM). For these models, we derive maximum likelihood estimators for the reduction and use them to predict the response via nonparametric rules for forward regression. Through simulations and real data applications, we demonstrate the effectiveness of our approach for spatial data prediction.