Globally robust inference for the location and simple regression

JORGE G. ADROVER, MATIAS SALIBIAN-BARRERA AND RUBEN H. ZAMAR

JOURNAL OF STATISTICAL PLANNING AND INFERENCE

ELSEVIER SCIENCE BV

Año: 2004 vol. 119 p. 353 - 375

0378-3758

We de2ne globally robust con2dence intervals and p-values for the location and simple linear regression models. The need for robust inference has been noticed and partially addressed in the statistical literature (see for example the book by Barnett and Lewis, Outliers in Statistical Data, Wiley, New York, 1994 and references therein). We construct intervals that are stable in the sense of achieving coverages near the nominal ones even in the presence of outliers and other departures from the parametric model. Moreover, our intervals are informative in the sense of having relatively short lengths. These globally robust con2dence intervals constitute an improvement over previous robust intervals which do not take into account the potential bias of the estimates.p-values for the location and simple linear regression models. The need for robust inference has been noticed and partially addressed in the statistical literature (see for example the book by Barnett and Lewis, Outliers in Statistical Data, Wiley, New York, 1994 and references therein). We construct intervals that are stable in the sense of achieving coverages near the nominal ones even in the presence of outliers and other departures from the parametric model. Moreover, our intervals are informative in the sense of having relatively short lengths. These globally robust con2dence intervals constitute an improvement over previous robust intervals which do not take into account the potential bias of the estimates.