Robustifying Likelihoods by Optimistically Re-weighting Data
针对似然推断中模型误设导致的脆弱性问题，提出乐观加权似然法，通过在经验测度的距离邻域内选择最友好的数据生成过程来增强稳健性，并应用于混合模型和回归。
Likelihood-based inferences have been remarkably successful in wide-spanning application areas. However, even after due diligence in selecting a good model for the data at hand, there is inevitably some amount of model misspecification: outliers, data contamination or inappropriate parametric assumptions such as Gaussianity mean that most models are at best rough approximations of reality. A significant practical concern is that for certain inferences, even small amounts of model misspecification may have a substantial impact; a problem we refer to as brittleness. This article attempts to address the brittleness problem in likelihood-based inferences by choosing the most model friendly data generating process in a distance-based neighborhood of the empirical measure. This leads to a new Optimistically Weighted Likelihood (OWL), which robustifies the original likelihood by formally accounting for a small amount of model misspecification. Focusing on total variation (TV) neighborhoods, we study theoretical properties, develop estimation algorithms and illustrate the methodology in applications to mixture models and regression.