Smoothed Local L-Estimation With an Application

The Nadaraya-Watson regression estimator is known to be highly sensitive to the presence of outliers in the sample. A possible robustification consists in using local L-estimates of regression. Whereas the local L-estimation is traditionally done using the empirical conditional distribution function, Tamine et al. (2003) have recently proposed to use a smoothed conditional distribution function instead. This work studies computational aspects and small-sample properties of the smoothed L-estimation approach. The smoothed nonparametric L-estimator is applied to the estimation of the so-called implied volatilities, which describe the conditional variance of high-frequency financial time series (such as exchange rates or stock prices) inferred from the prices of related financial derivatives.