Linearized Maximum Rank Correlation Estimation

Guohao Shen, Kani Chen, Jian Huang, Yuanyuan Lin

Research output: Journal article publicationJournal articleAcademic researchpeer-review

5 Citations (Scopus)

Abstract

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.

Original languageEnglish
Pages (from-to)187-203
Number of pages17
JournalBiometrika
Volume110
Issue number1
DOIs
Publication statusPublished - Mar 2023

Keywords

  • Censored data
  • Closed-form solution
  • Linearized maximum rank correlation
  • Single-index model

ASJC Scopus subject areas

  • Statistics and Probability
  • General Mathematics
  • Agricultural and Biological Sciences (miscellaneous)
  • General Agricultural and Biological Sciences
  • Statistics, Probability and Uncertainty
  • Applied Mathematics

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