TY - JOUR

T1 - Estimation of the spatial weighting matrix for regular lattice data—An adaptive lasso approach with cross-sectional resampling

AU - Merk, M.S.

AU - Otto, P.

PY - 2022/1/23

Y1 - 2022/1/23

N2 - 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 (Formula presented.) concentrations and show that estimating the spatial dependence structure contrary to using prespecified weights matrices improves the prediction accuracy considerably.

AB - 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 (Formula presented.) concentrations and show that estimating the spatial dependence structure contrary to using prespecified weights matrices improves the prediction accuracy considerably.

UR - http://www.scopus.com/inward/record.url?scp=85115621249&partnerID=8YFLogxK

U2 - 10.1002/env.2705

DO - 10.1002/env.2705

M3 - Article

VL - 33

JO - ENVIRONMETRICS

JF - ENVIRONMETRICS

SN - 1180-4009

IS - 1

M1 - e2705

ER -