Local Smoothing with Robustness against Outlying Predictors

Outlying pollutant concentration data are frequently observed in time series studies conducted to investigate the effects of atmospheric pollution and mortality/morbidity. These outliers may severely affect the estimation procedures and even generate unexpected results like a protective effect of pollution. Although robust methods have been proposed to downweight the effect of outliers in the response variable distribution, little has been done to handle outlying explanatory variable values. We consider a robust local polynomial smoothing technique which may be useful for such purposes. It is based on downweighting points with a small design density and may also be used as a diagnostic tool to identify outliers. Using data from a study conducted in São Paulo, Brazil, we show how an unexpected form of the relative risk curve of mortality attributable to pollution by SO_2 obtained via nonrobust methods may be completely reversed when the proposed technique is employed