Minimum entropy estimation in semi parametric models

The paper is a continuation of earlier work (Pronzato and Thierry, Proc. 20th Int. Workshop on Bayesian Inference and Maximum Entropy Methods in Science and Engineering, p.169-80, 2001; Proc. ICASSP, 2001): 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 (Stein, C., 1956; Stone, C.J., 1975; Bickel, P.J., 1982;. Manski, C.F, 1984). Connections and differences with previous work are indicated. Numerical results illustrate that asymptotic efficiency is not necessarily in conflict with robustness.