We propose a new robust estimator of the regression coefficients in a linear regression model. The proposed estimator is the only robust estimator based on integration rather than optimization. It allows for dependence between errors and regressors, is n-consistent, and asymptotically normal. Moreover, it has the best achievable breakdown point of regression invariant estimators, has bounded gross error sensitivity, is both affine invariant and regression invariant, and the number of operations required for its computation is linear in n. An extension would result in bounded local shift sensitivity, also.
All Science Journal Classification (ASJC) codes
- Statistics and Probability
- Numerical Analysis
- Statistics, Probability and Uncertainty