Resampling permutations in linear regression

                            by
 
                    Krzysztof Podgorski

         Indiana University - Purdue University 
                    at Indianapolis

                        Abstract 
Resampling random permutations of residuals to the least
square fit in linear regression posses surprisingly robust
properties. They give foundation to a bootstrap method
which is applicable to regression with errors not
necessarily having finite moments. The method is extended
to the reduced regression model which comes from the
original one by removing errors corresponding to the extreme
values. The deletion is based on ranks of computable
residuals. This leads to a concrete estimation algorithm
which is robust on extremal values of errors and competitive
to other robust methods. For models with Gauss, Cauchy and
other stable errors numerical analysis reveals that our
bootstrap confidence intervals are usually narrower than ones
based on M-estimation or the least trimmed squares method.