Choosing a robustness tuning parameter

摘要

A novel method is proposed for choosing the tuning parameter associated with a family of robust estimators. It consists of minimising estimated mean squared error, an approach that requires pilot estimation of model parameters. The method is explored for the family of minimum distance estimators proposed by [Basu, A., Harris, I.R., Hjort, N.L. and Jones, M.C., 1998, Robust and efficient estimation by minimising a density power divergence. Biometrika, 85, 549-559.] Our preference in that context is for a version of the method using the L_2 distance estimator [Scott, D.W., 2001, Parametric statistical modeling by minimum integrated squared error. Technometrics, 43, 274-285.] as pilot estimator.