The present paper offers two methods of adaptive estimation of linear regression models. A common assumption for both of them is symmetry (of distribution of errors). Although the symmetry (or at least precise symmetry) doesn’t take place so frequently as it is sometimes believed, if it can be assumed, it is advantageous not only from a technical point of view but it may clarify also philosophy behind the mathematical theory. E.g., for the location problem – under symmetry – the mean (if exists), median, modus (if unimodal distribution) and center of symmetry coincide and hence there is no problem what is to be understood under location parameter and estimation. Moreover the experiences of practitioners with symmetry are so good that sometimes they prefer to find (a simple) one-to-one transformation of data bringing them to symmetry and only then they apply an estimating procedure (naturally with succeeding retransformation). But even if we accept such kind of arguments we have to realize that the situation for the location model is much simpler than for the regression model, because we may e.g. test whether the data are symmetric or not, or even we may estimate “a true” model.
For the entire collection see [Zbl 0831.00021].