Robust regression and outlier detection
Robust regression and outlier detection
Efficient algorithms for maximum regression depth
SCG '99 Proceedings of the fifteenth annual symposium on Computational geometry
An optimal algorithm for hyperplane depth in the plane
SODA '00 Proceedings of the eleventh annual ACM-SIAM symposium on Discrete algorithms
Robustness of deepest regression
Journal of Multivariate Analysis
Computing location depth and regression depth in higher dimensions
Statistics and Computing
Depth estimators and tests based on the likelihood principle with application to regression
Journal of Multivariate Analysis
Calculation of simplicial depth estimators for polynomial regression with applications
Computational Statistics & Data Analysis
Computational Statistics & Data Analysis
Distribution-free tests for polynomial regression based on simplicial depth
Journal of Multivariate Analysis
Tests for multiple regression based on simplicial depth
Journal of Multivariate Analysis
Depth notions for orthogonal regression
Journal of Multivariate Analysis
The least trimmed quantile regression
Computational Statistics & Data Analysis
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Deepest regression (DR) is a method for linear regression introduced by P. J. Rousseeuw and M. Hubert (1999, J. Amer. Statis. Assoc. 94, 388-402). The DR method is defined as the fit with largest regression depth relative to the data. In this paper we show that DR is a robust method, with breakdown value that converges almost surely to 1/3 in any dimension. We construct an approximate algorithm for fast computation of DR in more than two dimensions. From the distribution of the regression depth we derive tests for the true unknown parameters in the linear regression model. Moreover, we construct simultaneous confidence regions based on bootstrapped estimates. We also use the maximal regression depth to construct a test for linearity versus convexity/concavity. We extend regression depth and deepest regression to more general models. We apply DR to polynomial regression and show that the deepest polynomial regression has breakdown value 1/3. Finally, DR is applied to the Michaelis-Menten model of enzyme kinetics, where it resolves a long-standing ambiguity.