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Abstract
Adaptive penalized splines via radial basis are constructed to estimate regression functions and their derivatives. A weight vector based on the range of observations is embedded into the penalty matrix, which remarkably improves the adaptability of the penalized spline smoothing model. Fast computation and comparison with traditional spline models are studied, and the empirical results and simulations show that the new method outperforms smoothing splines, traditional penalized splines and local polynomial smoothing when estimating regression functions and their derivatives, particularly when the observations have inhomogeneous variation.
Mathematics Subject Classification (2000):
Additional information
Funding
This research was supported by the National Science Foundation of China (Grant NO. 11671012), the Key University Science Research Project of Anhui, China (Grant NO. KJ2017A028) and the Open Project Program of the School of Mathematical Sciences of Anhui University (Grant NO. Y01002431). The authors are grateful to the editor and referees for their valuable comments and insightful suggestions, which were used to improve the quality of this paper.