  Spatially misaligned data, where the response and covariates are observed at
different spatial locations, commonly arise in many environmental studies. Much
of the statistical literature on handling spatially misaligned data has been
devoted to the case of a single covariate and a linear relationship between the
response and this covariate. Motivated by spatially misaligned data collected
on air pollution and weather in China, we propose a cokrig-and-regress (CNR)
method to estimate spatial regression models involving multiple covariates and
potentially non-linear associations. The CNR estimator is constructed by
replacing the unobserved covariates (at the response locations) by their
cokriging predictor derived from the observed but misaligned covariates under a
multivariate Gaussian assumption, where a generalized Kronecker product
covariance is used to account for spatial correlations within and between
covariates. A parametric bootstrap approach is employed to bias-correct the CNR
estimates of the spatial covariance parameters and for uncertainty
quantification. Simulation studies demonstrate that CNR outperforms several
existing methods for handling spatially misaligned data, such as
nearest-neighbor interpolation. Applying CNR to the spatially misaligned air
pollution and weather data in China reveals a number of non-linear
relationships between PM$_{2.5}$ concentration and several meteorological
covariates.
