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Title: Stein discrepancy methods for robust estimation Authors:  Emre Barut - George Washington University (United States) [presenting]
Abstract: All statistical procedures highly depend on the modeling assumptions and how close these assumptions are to reality. This dependence is critical: Even the slightest deviation from assumptions can cause major instabilities during statistical estimation. In order to mitigate issues arising from model mismatch, numerous methods have been developed in the area of robust statistics. However, these approaches are aimed at specific problems, such as heavy tailed or correlated errors. The lack of a holistic framework in robust regression results in a major problem for the data practitioner. That is, in order to build a robust statistical model, possible issues in the data have to be found and understood before conducting the analysis. In addition, the practitioner needs to have an understanding of which robust models can be applied in which situations. We propose a new framework for parameter estimation, which is given as the empirical minimizer of a second order U-statistic. When estimating parameters in the exponential family, the estimate can be obtained by solving a quadratic convex problem. For parameter estimation, our approach significantly improves upon MLE when outliers are present, or when the model is misspecified. Furthermore, we show how the new estimator can be used to efficiently fit to distributions with unknown normalizing constants. Extensions of our method for regression problems and implications for statistical modeling are discussed.