Choosing a robustness tuning parameter

Warwick, J. and Jones, M.C. (2005). Choosing a robustness tuning parameter. Journal of Statistical Computation and Simulation, 75(7) pp. 581–588.



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.

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