Robust recursive Lp estimation

Outlier-contaminated normal errors in regression problems are modelled by exponential power distributions and the resulting maximum likelihood estimators are shown to involve L_p minimisations (11+ estimation is minimax outlier-robust and minimax covariance-robust over the neighbourhood of exponential power distributions. Efficiency loss is negligible. Recursive gradient-type L_p estimators are derived and shown to be convergent and consistent. The major limitation outlier robustness is seen to be the requirement for convergence of the recursive minimisation. The algorithm is validated with an application in adaptive control.