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Adaptive quantile regression with precise risk bounds. (English) Zbl 1369.62068
Summary: An adaptive local smoothing method for nonparametric conditional quantile regression models is considered in this paper. Theoretical properties of the procedure are examined. The proposed method is fully adaptive in the sense that no prior information about the structure of the model is assumed. The fully adaptive feature not only allows varying bandwidths to accommodate jumps or instantaneous slope changes, but also allows the algorithm to be spatially adaptive. Under general conditions, precise risk bounds for homogeneous and heterogeneous cases of the underlying conditional quantile curves are established. An automatic selection algorithm for locally adaptive bandwidths is also given, which is applicable to higher dimensional cases. Simulation studies and data analysis confirm that the proposed methodology works well.
MSC:
62G07 Density estimation
62G05 Nonparametric estimation
62G20 Asymptotic properties of nonparametric inference
62P25 Applications of statistics to social sciences
62G35 Nonparametric robustness
Software:
AWS
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