M-estimators for Isotonic Regression

EMRIQUE E. ALVAREZ; VICTOR J. YOHAI

JOURNAL OF STATISTICAL PLANNING AND INFERENCE

ELSEVIER SCIENCE BV

Lugar: Amsterdam; Año: 2012 vol. 142 p. 2351 - 2368

0378-3758

In this paper we propose a family of robust estimates for isotonic regression: isotonic M-estimators. We show that their asymptotic distribution is, up to an scalar factor, the same as that of Brunk’s classical isotonic estimator. We also derive the influence function and the breakdown point of these estimates. Finally we perform a Monte Carlo study that shows that the proposed family includes estimators that are simultaneously highly efficient under Gaussian errors and highly robust when the error distribution has heavy tails.