Department of Mathematics
Variance estimation is an important topic in nonparametric regression. In this paper, we propose a pairwise regression method for estimating the residual variance. Specifically, we regress the squared difference between observations on the squared distance between design points, and then estimate the residual variance as the intercept. Unlike most existing difference-based estimators that require a smooth regression function, our method applies to regression models with jump discontinuities. Our method also applies to the situations where the design points are unequally spaced. Finally, we conduct extensive simulation studies to evaluate the finite-sample performance of the proposed method and compare it with some existing competitors.
difference-based estimator, jump point, non-uniform design, nonparametric regression, pairwise regression, residual variance
Source Publication Title
Journal of Applied Statistics
Taylor & Francis
This is an Accepted Manuscript of an article published by Taylor & Francis in Journal of Applied Statistics in March 2014, available online: http://www.tandfonline.com/10.1080/02664763.2013.842962.
This researchwas supported by HongKongRGCgrantHKBU202711, and HongKong Baptist University grantsFRG2/10- 11/020 and FRG2/11-12/110. The authors thank the editor, the associate editor, and two referees for their helpful comments and suggestions that have substantially improved the paper.
Link to Publisher's Edition
Dai, W., & Tong, T. (2014). Variance estimation in nonparametric regression with jump discontinuities. Journal of Applied Statistics, 41 (3), 530-545. https://doi.org/10.1080/02664763.2013.842962