ADAPTIVE ESTIMATION IN LINEAR-REGRESSION MODEL .2. ASYMPTOTIC NORMALITY

Asymptotic representation of an adaptive estimator based on Beran's idea of minimizing Hellinger distance is derived. It is shown that the estimator is asymptotically normal but not efficient. From the practical point of view the approach may be useful because it selects a model with distribution of residuals symmetric ''as much as possible' (in the sense of Hellinger distance applied on F(x) and 1 - F(x)). It is not difficult to construct a numerical examples showing that sometimes it is the only way how to find proper model.