Robust recursive Lp estimation

Abstract

Outlier-contaminated normal errors in regression problems are modelled by exponential power distributions and the resulting maximum likelihood estimators are shown to involve Lp minimisations (1 < P ,,2). It is shown that La estimation is minimax outlier-robust and minimax covariance-robust over the neighbourhood of exponential power distributions. Efficiency loss is negligible. Recursive gradient-type Lp estimators are derived and shown to be convergent and consistent. The major limitation on outlier robustness is seen to be the requirement for convergence of the recursive minimisation. The algorithm is validated with an application in adaptive control.

MixedLpEstimators Variety for Model Order Reduction in Control Oriented System Identification

“…Finally, most of the time, ∞ norm is used to the model reduction for robust control [6] with the restricted case where the model parameters number is limited. The norms are widely used in many domains [7,8]. Even though the formal framework presents some difficulties, previous works show the interest to use these estimators.…”

Proceedings of the Third European Conference on Mathematics in Industry

“…1 if the errors are uncorrelated[McMichael, 1988]. 1 if the errors are uncorrelated[McMichael, 1988].…”

From batch to recursive outlier-robust identification of non-linear dynamic systems with neural networks

“…As p decreases from 2 (normal distribution) to 1, the distribution develops longer thicker tails and outliers are more probable. Such a priori knowledge of the noise distribution leads to ML estimators involving Lp criterion minimisation [16]. The following case cost function is thus employed in (5) and leads to a modification of ( le( k)l -3 6 (1 -p/2) )' (E( k)l2 36 &(k)2 (p/2)' (36)'-*…”