A model where the least trimmed squares estimator is maximum likelihood

• 成果类型: Article
• 署名作者: Berenguer-Rico, Vanessa; Johansen, Soren; Nielsen, Bent
• 署名单位: University of Oxford; University of Copenhagen; University of Oxford
• 刊物名称: JOURNAL OF THE ROYAL STATISTICAL SOCIETY SERIES B-STATISTICAL METHODOLOGY
• ISSN/ISSBN: 1369-7412
• DOI: 10.1093/jrsssb/qkad028
• 发表日期: 2023
• 页码: 886-912
• 关键词: time-series; regression; algorithms; point

摘要

The least trimmed squares (LTS) estimator is a popular robust regression estimator. It finds a subsample of h 'good' observations among n observations and applies least squares on that subsample. We formulate a model in which this estimator is maximum likelihood. The model has 'outliers' of a new type, where the outlying observations are drawn from a distribution with values outside the realized range of h 'good', normal observations. The LTS estimator is found to be h(1/2) consistent and asymptotically standard normal in the location-scale case. Consistent estimation of h is discussed. The model differs from the commonly used e-contamination models and opens the door for statistical discussion on contamination schemes, new methodological developments on tests for contamination as well as inferences based on the estimated good data.