Dimension reduction provides a useful tool for analyzing high-dimensional data. The
recently developed envelope method is a parsimonious version of the classical multivariate
regression model that identifies a minimal reducing subspace of the responses. However,
existing envelope methods assume an independent error structure in the model. While the
assumption of independence is convenient, it does not address the additional complications
associated with spatial or temporal correlations in the data. Therefore, we propose a Spatial …

Dimension reduction provides a useful tool for analyzing high dimensional data. The
recently developed\textit {Envelope} method is a parsimonious version of the classical
multivariate regression model through identifying a minimal reducing subspace of the
responses. However, existing envelope methods assume an independent error structure in
the model. While the assumption of independence is convenient, it does not address the
additional complications associated with spatial or temporal correlations in the data. In this …