A0297
Title: Optimal-$k$ difference sequence in nonparametric regression
Authors: Wenlin Dai - Renmin University of China (China) [presenting]
Xingwei Tong - Beijing Normal University (China)
Tiejun Tong - Hong Kong Baptist University (Hong Kong)
Abstract: Difference-based methods have been attracting increasing attention in nonparametric regression, particularly for estimating the residual variance. To implement the estimation, one needs to choose an appropriate difference sequence, mainly between the optimal difference sequence and the ordinary difference sequence. The difference sequence selection is a fundamental problem in nonparametric regression, and it has remained a controversial issue for over three decades. The aim is to tackle this challenging issue from a unique perspective, namely by introducing a new difference sequence called the optimal-$k$ difference sequence. The new difference sequence not only provides a better balance between the bias-variance trade-off but also dramatically enlarges the existing family of difference sequences that includes the optimal and ordinary difference sequences as two important special cases. Further, it is demonstrated, by both theoretical and numerical studies, that the optimal-$k$ difference sequence has been pushing the boundaries of the knowledge in difference-based methods in nonparametric regression, and it always performs the best in practical situations.
