O método de máxima Lq-verossimilhança em modelos com erros de medição
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In this work we consider a new estimator proposed by Ferrari & Yang (2010), called the maximum Lq-likelihood estimator (MLqE), to estimate the parameters of the measurement error models, in particular, the structural model. The new estimator extends the classical maximum likelihood estimator (MLE) and its based on the minimization, by means of the Kullback-Leibler (KL) divergence, of the discrepancy between a distribuiton in a family and one that modifies the true distribution by the degree of distortion q. Depending on the choice of q, the transformed distribution can diminish or emphasize the role of extreme observations, unlike the ML method that equally weights each observation. For small and moderate sample sizes, the MLqE can trade bias for precision, causing a reduction of the mean square error (MSE). The structural model has the characteristic of non-identifiability. For this reason, we must make assumptions on the parameters to overcome the non-identifiability. We perform a analytical study and a simulation study to compare MLqE and MLE. To gauge performance of the estimators, we compute measures of overall performance, bias, standard deviation, standard error, MSE, probability of coverage and length of confidence intervals.