Abstract: We consider the problem of estimation of regression coefficients under general classes of error densities without assuming classical regularity conditions. Optimal orders of convergence rates of regression-equivariant estimators are established and shown to be attained in general by estimators based on judicious choices of . We develop a procedure for choosing adaptively to yield estimators that converge at approximately optimal rates. The procedure consists of a special algorithm to automatically select the correct mode of estimation and the out of bootstrap to consistently estimate the log mean squared error of the estimator. Our proposed adaptive estimator is compared with other adaptive and non-adaptive estimators in a simulation study, that confirms superiority of our procedure.
Key words and phrases: Adaptive, Lp estimator, m out of n bootstrap, ratewise efficient, regression.