Robust estimation in functional comparative calibration models via maximum Lq-likelihood

. A fully parametric estimation procedure is proposed for robust estimation of the structural parameter in a functional comparative calibration model, under normality. The proposed estimator is obtained, based on maximum L q -likelihood approach, ﬁrst re-placing the incidental parameters by estimators depending on the structural parameter. The estimator, called ML q E, depends on a single distortion parameter q , which controls the bal-ance between robustness and efﬁciency. If q tends to 1, the maximum likelihood estimator (MLE) is obtained. The estimation procedure can be implemented easily by a simple and fast re-weighting algorithm. For applying the method to practical and real-data scenarios, a data-based choice of an appropriate value of q is proposed. Consistency and asymptotic normality is established and the covariance matrix is given. The inﬂuence function is derived, to show the local robustness properties. Theoretical properties, ease of imple-mentabiliy and empirical results on simulated and real data show the satisfactory behavior of the ML q E and its vantages over the MLE in presence of observations discordant with the assumed model.