M-Quantiles combine the robustness and interpretability of quantiles with the flexibility and intuitive estimation of expectiles. They allow for an iteratively weighted least squares estimation including quadratic penalties to incorporate a semiparametric model. The inclusion of p-splines and spatial effects, like Markov random fields, is possible. And by definition their estimate is still robust against outliers. However, this is only true for homoscedastic scenarios. In heteroscedastic cases the distinction between outliers and “trustable” observations is likely to fail. Here, we introduce adaptive M-Quantile regression models to overcome this problem by replacing the tuning constant of the M-Quantile estimation with a robustness curve. The latter is constructed from the scale part of a location-scale model. Our findings will be analysed in a simulation study and made available as R-package “Mreg”.
Adaptive semiparametric M-quantile regression
RANALLI, Maria Giovanna;
2012
Abstract
M-Quantiles combine the robustness and interpretability of quantiles with the flexibility and intuitive estimation of expectiles. They allow for an iteratively weighted least squares estimation including quadratic penalties to incorporate a semiparametric model. The inclusion of p-splines and spatial effects, like Markov random fields, is possible. And by definition their estimate is still robust against outliers. However, this is only true for homoscedastic scenarios. In heteroscedastic cases the distinction between outliers and “trustable” observations is likely to fail. Here, we introduce adaptive M-Quantile regression models to overcome this problem by replacing the tuning constant of the M-Quantile estimation with a robustness curve. The latter is constructed from the scale part of a location-scale model. Our findings will be analysed in a simulation study and made available as R-package “Mreg”.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
