Minimum entropy estimation in semi parametric models

This paper is a continuation of the work initiated in [1, 2]: we estimate parameters in a regression model, linear or not, by minimizing (an estimate of) the entropy of the symmetrized residuals, obtained by a kernel estimation of their distribution. The objective is to obtain efficiency in the absence of knowledge of the density f of the observation errors, which is called adaptive estimation, see in particular [3, 4, 5] and the review paper [6]. Connections and differences with previous work are indicated. Numerical results illustrate that asymptotic efficiency is not necessarily in conflict with robustness.