Minimum-Entropy Estimation in Semi-Parametric Models ## AbstractIn regression problems where the density f of the errors is not known, maximum likelihood is unapplicable, and the use of alternative techniques like least squares or robust M-estimation generally implies inefficient estimation of the parameters. The search for adaptive estimators, that is, estimators that remain asymptotically efficient independently of the knowledge of f, has received a lot of attention, see in particular (Stein56, Stone75, Bickel82) and the review paper (Manski84). The paper considers a minimum-entropy parametric estimator that minimizes an estimate of the entropy of the distribution of the residuals. A first construction connects the method with the Stone-Bickel approach, where the estimation is decomposed into two steps. Then we consider a direct approach that does not involve any preliminary root(n)-consistent estimator. Some results are given that illustrate the good performance of minimum-entropy estimation for reasonable sample sizes when compared to standard methods, in particular concerning robustness in the presence of outliers.
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