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C. Mühlmann, H. Oja, K. Nordhausen:
"Supervised dimension reduction for spatial data";
Vortrag: ÖSG Statistiktage, Wien; 24.10.2019 - 25.10.2019.

In a regression context a higher number of predictors makes modeling very demanding and increases the computational cost significantly. Therefore, reducing the number of predictors without loosing information on the response variable prior building the actual regression model is a promising approach. Such methods are denoted as supervised dimension reduction (SDR). Sliced inverse regression (SIR) is one popular SDR method method that is well established for iid data (Li, 1991). SIR was recently also extended to the time series case (Matilainen et al., 2017). However, there seem not to be any supervised dimension reduction methods for the spatial data case.
Measurements taken on different spatial locations are a common type of data. It is natural to assume that measurements that are closer together show more similarity than measurements taken far apart. Similarly, in a regression context it is natural to assume that the response variable is not only depending on the on-site predictors but also on predictors in the vicinity. There are many regression models taking into account spatial dependence. Issues with a high number of predictors are still remaining, hence, supervised dimension reduction for spatial data would be a valuable tool.
In our contribution we extend SIR to the spatial data case (Mühlmann et al., 2019). We focus on measurements that are recorded on a grid structure and formulate SIR in a blind source separation model to extract a subspace of the predictors that caries the most information of the response variable. Furthermore, we present practical guidelines on how to choose the dimension of the subspace as well as spatial lags of interest.