Some Adaptive Procedures for Regression Models

Regression models belong to those statistical models, which are applied to extremely diverse types of data in many fields of quantitative relationships. Normally distributed errors are usually assumed and least squares estimates are applied. It is known that for normally distributed errors the least squares estimates are optimal in several respects, while for nonnormally distributed errors these estimates are ineffective and, moreover, they are sensitive to outlying observations. Classes of estimators were developed which show a reasonable behavior for comparatively large families of error distributions and which are not too sensitive to the outliers. Such estimators are usually called robust. Some of these estimators can be adapted with respect to the data In such a way that the resulting estimates are in some sense optimal; these estimators are called adaptive. The aim of this paper is to present some adaptive estimates for regression models.