|
Abstract:
|
Is there a one-stage estimator that can achieve resistance, statistical accuracy and asymptotic efficiency simultaneously? We address this problem by proposing the resistant regression with an adaptively growing robusti fication parameter, hence the name, adaptive resistant regression. The key observation is, by taking the resistant parameter at a proper order, the proposed estimator automatically achieves high accuracy and high efficiency. Surprisingly, at the same time, it does not lose resistance: the proposed estimator achieves the breakdown point of 1=2 asymptotically. Computationally, we formulate the problem as a quadratic mixed integer programming problem and propose a fast randomized algorithm for fast computation. Numerical examples lend strong support to our methodology and theory.
|
