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C. Mühlmann, H. Oja, K. Nordhausen:
"Supervised dimension reduction for spatial data";
Talk: "12th International Conference of the ERCIM WG on Computational and Methodological Statistics (CMStatistics 2019)", London; 2019-12-14 - 2019-12-16.

In regression tasks a higher number of predictors makes modeling very demanding and increases the computational cost significantly. Supervised dimension reduction (SDR) addresses these issues by reducing the number of predictors prior building the actual model. Sliced inverse regression (SIR) is one popular SDR method that is well established for iid data. SIR was recently also extended to the time series case. However, there seem not to be any SDR methods for spatial data. In the spatial data context, it is natural to assume that measurements that are closer together show more similarity than measurements taken far apart. Similarly, in spatial regression the response variable maybe not only depending on the on-site predictors but also on predictors in the vicinity. There are many regression models considering spatial dependence but issues with a high number of predictors are still remaining. We extend SIR to spatial data recorded on a grid by formulating it in a blind source separation model to extract a subspace of the neighboring predictors that carries the most information of the response variable. Furthermore, practical guidelines on how to choose the dimension of the subspace as well as spatial lags of interest are given.