A0179
Title: Optimal-k sequence for difference-based methods in nonparametric regression
Authors: Tiejun Tong - Hong Kong Baptist University (Hong Kong) [presenting]
Abstract: Difference-based methods have been attracting increasing attention in nonparametric regression, in particular 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. This difference sequence selection is a fundamental problem in nonparametric regression, and it remains unresolved until recently. We propose to further advance the difference sequence selection from another unique perspective, which creates a new family of difference sequences called the optimal-k sequence. Our proposed difference sequence not only provides a better bias-variance trade-off but also includes the optimal and the ordinary difference sequences as two important special cases. Through theoretical and numerical studies, we demonstrate that the optimal-k sequence has been pushing the boundaries of our knowledge in difference-based methods in nonparametric regression, and more importantly, it always performs the best in practical situations.
