In this paper we propose a new method of local linear adaptive smoothing for nonparametric conditional quantile regression. Some theoretical properties of the procedure are investigated. Then we demonstrate the perfor...In this paper we propose a new method of local linear adaptive smoothing for nonparametric conditional quantile regression. Some theoretical properties of the procedure are investigated. Then we demonstrate the performance of the method on a simulated example and compare it with other methods. The simulation results demonstrate a reasonable performance of our method proposed especially in situations when the underlying image is piecewise linear or can be approximated by such images. Generally speaking, our method outperforms most other existing methods in the sense of the mean square estimation （MSE） and mean absolute estimation （MAE） criteria. The procedure is very stable with respect to increasing noise level and the algorithm can be easily applied to higher dimensional situations.展开更多
基金supported by the National Natural Science Foundation of China (No.10871201)the Major Project of Humanities Social Science Foundation of Ministry of Education (No. 08JJD910247)+2 种基金Key Project of Chinese Ministry of Education (No.108120)Beijing Natural Science Foundation (No. 1102021)Graduate Research Foundation of Ren Min University of China (Adaptive Composite Quantile Regression Model and Bootstrap Confidence Interval Theory and Applications (No.11XNH108))
文摘In this paper we propose a new method of local linear adaptive smoothing for nonparametric conditional quantile regression. Some theoretical properties of the procedure are investigated. Then we demonstrate the performance of the method on a simulated example and compare it with other methods. The simulation results demonstrate a reasonable performance of our method proposed especially in situations when the underlying image is piecewise linear or can be approximated by such images. Generally speaking, our method outperforms most other existing methods in the sense of the mean square estimation （MSE） and mean absolute estimation （MAE） criteria. The procedure is very stable with respect to increasing noise level and the algorithm can be easily applied to higher dimensional situations.
