Robust estimation under heavy contamination using unnormalized models
提出一种基于评分规则的新方法，同时估计统计模型参数和污染比例，并检测异常值，适用于回归问题中的复杂异质污染。
Contamination caused by outliers is inevitable in data analysis, and robust statistical methods are often needed. In this paper we develop a new approach for robust data analysis on the basis of scoring rules. A scoring rule is a discrepancy measure to assess the quality of probabilistic forecasts. We propose a simple method of estimating not only parameters in the statistical model but also the contamination ratio, i.e., the ratio of outliers. The outliers are detected based on the estimated contamination ratio. For this purpose, we use scoring rules with extended statistical models called unnormalized models. Regression problems are also considered. We study complex heterogeneous contamination wherein the contamination ratio in a response variable may depend on covariate variables, and propose a simple method to estimate a robust regression function and expected contamination ratio. Simulation studies demonstrate the effectiveness of our method.