Multi-class estimation for high-dimensional econometric models

Retailers would like to forecast sales for a large number of categories, such as soft drinks and soap, based on a large number of demographical predictors. These data are available not for just one country in which they operate, but for several countries, called "classes". Today's business practice would be to either forecast sales using one large model, thereby ignoring the differences between the countries, or forecast sales using separate models, one for each country, thereby ignoring the similarities between the countries. These approaches are not the most efficient. Since the countries serve the same customer market, a first and key desirable property of the modeling approach would be to borrow strength across countries by jointly forecasting sales for all countries and to encourage estimates to be similar across countries. Secondly, a retailer would prefer a so called "sparse" modeling approach that allows to distinguish important from unimportant predictors. Thirdly, forecasts should remain reliable, or "robust", in the presence of atypical countries. Detection of these "outlying" countries is important to adopt a country-specific strategy that, for instance, avoids opening a new store in a country whose market is difficult to serve. This research project aims to develop such multi-class estimators for high-dimensional econometric models that allow joint, sparse and robust estimation of multiple models that share certain characteristics.