Estimation of the spatial weighting matrix for regular lattice data—An adaptive lasso approach with cross-sectional resampling

Merk, M. S. and Otto, P. (2022) Estimation of the spatial weighting matrix for regular lattice data—An adaptive lasso approach with cross-sectional resampling. Environmetrics, 33(1), e2705. (doi: 10.1002/env.2705)

Abstract

Spatial autoregressive models typically rely on the assumption that the spatial dependence structure is known in advance and is represented by a deterministic spatial weights matrix, although it is unknown in most empirical applications. Thus, we investigate the estimation of sparse spatial dependence structures for regular lattice data. In particular, an adaptive least absolute shrinkage and selection operator (lasso) is used to select and estimate the individual nonzero connections of the spatial weights matrix. To recover the spatial dependence structure, we propose cross-sectional resampling, assuming that the random process is exchangeable. The estimation procedure is based on a two-step approach to circumvent simultaneity issues that typically arise from endogenous spatial autoregressive dependencies. The two-step adaptive lasso approach with cross-sectional resampling is verified using Monte Carlo simulations. Eventually, we apply the procedure to model nitrogen dioxide concentrations and show that estimating the spatial dependence structure contrary to using prespecified weights matrices improves the prediction accuracy considerably.

• Item Type: Articles
• Status: Published
• Refereed: Yes
• Glasgow Author(s) Enlighten ID: Otto, Dr Philipp
• Authors: Merk, M. S., and Otto, P.
• College/School: College of Science and Engineering > School of Mathematics and Statistics > Statistics
• Journal Name: Environmetrics
• Publisher: Wiley
• ISSN: 1180-4009
• ISSN (Online): 1099-095X
• Published Online: 23 January 2022
• Copyright Holders: Copyright © 2021 The Authors.
• First Published: First published in Environmetrics 33(1):e2705
• Publisher Policy: Reproduced under a Creative Commons license