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.