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

Abstract

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 Lq-likelihood approach, first replacing the incidental parameters by estimators depending on the structural parameter. The estimator, called MLqE, depends on a single distortion parameter q, which controls the balance 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 reweighting 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 implementabiliy and empirical results on simulated and real data show the satisfactory behavior of the MLqE and its vantages over the MLE in presence of observations discordant with the assumed model.