Estimation of conditional mean by the linear combination of quantile regression under heteroscedastic asymmetric errors

摘要

We investigate regression problems when the error distributions are asymmetric and heavy-tail. If the error distribution is symmetric around the mean value, traditional robust estimators are helpful by reducing the ef-fect of outliers equally from both sides of the distribution. Under asymmetric heavy-tail error distribution, however, those estimators are biased. We suggest a robust estimator which consists of the linear combination of quantile regressions. The estimator is derived from generalized location scale models and we show the robustness of the suggested estimator theoretically. Numerical experiments confirm the clear advantages of the suggested estimator comparing to traditional ones.