Smoothed L-estimation of Regression Function

The Nadaraya-Watson nonparametric estimator of regression is known to be highly sensitive to the presence of outliers in data.This sensitivity can be reduced, for example, by using local L-estimates of regression.Whereas the local L-estimation is traditionally done using an empirical conditional distribution function, we propose to use instead a smoothed conditional distribution function.The asymptotic distribution of the proposed estimator is derived under mild ¯-mixing conditions, and additionally, we show that the smoothed L-estimation approach provides computational as well as statistical ¯nite-sample improvements.Finally, the proposed method is applied to the modelling of implied volatilitynonparametric regression;L-estimation;smoothed cumulative distribution function

Smoothed L-estimation of Regression Function

The Nadaraya-Watson nonparametric estimator of regression is known to be highly sensitive to the presence of outliers in data.This sensitivity can be reduced, for example, by using local L-estimates of regression.Whereas the local L-estimation is traditionally done using an empirical conditional distribution function, we propose to use instead a smoothed conditional distribution function.The asymptotic distribution of the proposed estimator is derived under mild ¯-mixing conditions, and additionally, we show that the smoothed L-estimation approach provides computational as well as statistical ¯nite-sample improvements.Finally, the proposed method is applied to the modelling of implied volatilit

Smoothed L-Estimation of Regression Function

The Nadaraya-Watson estimator of regression is known to be highly sensitive to the presence of outliers in the sample. A possible way of robustication consists in using local L-estimates of regression. Whereas the local L-estimation is traditionally done using an empirical conditional distribution function, we propose to use instead a smoothed conditional distribution function. We show that this smoothed L-estimation approach provides computational as well as statistical finite sample improvements. The asymptotic distribution of the estimator is derived under mild β-mixing conditions

Smoothed L-estimation of regression function

The Nadaraya–Watson nonparametric estimator of regression is known to be highly sensitive to the presence of outliers in data. This sensitivity can be reduced, for example, by using local L-estimates of regression. Whereas the local L-estimation is traditionally done using an empirical conditional distribution function, we propose to use instead a smoothed conditional distribution function. The asymptotic distribution of the proposed estimator is derived under mild β-mixing conditions, and additionally, we show that the smoothed L-estimation approach provides computational as well as statistical finite-sample improvements. Finally, the proposed method is applied to the modelling of implied volatility

Smoothed L-estimation of regression function

The Nadaraya-Watson nonparametric estimator of regression is known to be highly sensitive to the presence of outliers in data. This sensitivity can be reduced, for example, by using local L-estimates of regression. Whereas the local L-estimation is traditionally done using an empirical conditional distribution function, we propose to use instead a smoothed conditional distribution function. The asymptotic distribution of the proposed estimator is derived under mild [beta]-mixing conditions, and additionally, we show that the smoothed L-estimation approach provides computational as well as statistical finite-sample improvements. Finally, the proposed method is applied to the modelling of implied volatility.