Linearized maximum rank correlation estimation

• 成果类型: Article
• 署名作者: Shen, Guohao; Chen, Kani; Huang, Jian; Lin, Yuanyuan
• 署名单位: Hong Kong Polytechnic University; Hong Kong University of Science & Technology; University of Iowa; Chinese University of Hong Kong
• 刊物名称: BIOMETRIKA
• ISSN/ISSBN: 0006-3444
• DOI: 10.1093/biomet/asac027
• 发表日期: 2023
• 页码: 187203
• 关键词: sliced inverse regression; single index models; generalized regression; Dimension Reduction; support recovery; selection

摘要

We propose a linearized maximum rank correlation estimator for the single-index model. Unlike the existing maximum rank correlation and other rank-based methods, the proposed estimator has a closed-form expression, making it appealing in theory and computation. The proposed estimator is robust to outliers in the response and its construction does not need knowledge of the unknown link function or the error distribution. Under mild conditions, it is shown to be consistent and asymptotically normal when the predictors satisfy the linearity of the expectation assumption. A more general class of estimators is also studied. Inference procedures based on the plug-in rule or random weighting resampling are employed for variance estimation. The proposed method can be easily modified to accommodate censored data. It can also be extended to deal with high-dimensional data combined with a penalty function. Extensive simulation studies provide strong evidence that the proposed method works well in various practical situations. Its application is illustrated with the Beijing PM 2.5 dataset.