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Robust estimation and inference for bivariate line‐fitting in allometry
Author(s) -
Taskinen Sara,
Warton David I.
Publication year - 2011
Publication title -
biometrical journal
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.108
H-Index - 63
eISSN - 1521-4036
pISSN - 0323-3847
DOI - 10.1002/bimj.201000018
Subject(s) - bivariate analysis , estimator , mathematics , robust regression , covariance , robust statistics , statistics , inference , principal component analysis , econometrics , computer science , artificial intelligence
In allometry, bivariate techniques related to principal component analysis are often used in place of linear regression, and primary interest is in making inferences about the slope. We demonstrate that the current inferential methods are not robust to bivariate contamination, and consider four robust alternatives to the current methods – a novel sandwich estimator approach, using robust covariance matrices derived via an influence function approach, Huber's M ‐estimator and the fast‐and‐robust bootstrap. Simulations demonstrate that Huber's M ‐estimators are highly efficient and robust against bivariate contamination, and when combined with the fast‐and‐robust bootstrap, we can make accurate inferences even from small samples.