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Many real-life data sets can be analyzed using Linear Mixed Models (LMMs).Since these are ordinarily based on normality assumptions, under smalldeviations from the model the inference can be highly unstable when theassociated parameters are estimated by classical methods. On the other hand,the density power divergence (DPD) family, which measures the discrepancybetween two probability density functions, has been successfully used to buildrobust estimators with high stability associated with minimal loss inefficiency. Here, we develop the minimum DPD estimator (MDPDE) for independentbut non identically distributed observations in LMMs. We prove the theoreticalproperties, including consistency and asymptotic normality. The influencefunction and sensitivity measures are studied to explore the robustnessproperties. As a data based choice of the MDPDE tuning parameter $\alpha$ isvery important, we propose two candidates as "optimal" choices, whereoptimality is in the sense of choosing the strongest downweighting that isnecessary for the particular data set. We conduct a simulation study comparingthe proposed MDPDE, for different values of $\alpha$, with the S-estimators,M-estimators and the classical maximum likelihood estimator, consideringdifferent levels of contamination. Finally, we illustrate the performance ofour proposal on a real-data example.

Robust Estimation under Linear Mixed Models: The Minimum Density Power Divergence Approach