Department of Mathematics
Over the past three decades, interest in cheap yet competitive variance estimators in nonparametric regression has grown tremendously. One family of estimators which has risen to meet the task is the difference-based estimators. Unlike their residual-based counterparts, difference-based estimators do not require estimating the mean function and are therefore popular in practice. This work further develops the difference-based estimators in the repeated measurement setting for nonparametric regression models. Three difference-based methods are proposed for the variance estimation under both balanced and unbalanced repeated measurement settings: the sample variance method, the partitioning method, and the sequencing method. Both their asymptotic properties and finite sample performance are explored. The sequencing method is shown to be the most adaptive while the sample variance method and the partitioning method are shown to outperform in certain cases.
Asymptotic normality, Difference-based estimator, Least squares, Nonparametric regression, Repeated measurements, Residual variance
Source Publication Title
Journal of Statistical Planning and Inference
Copyright © 2015 Elsevier B.V. All rights reserved.
Yanyuan Ma’s research was supported by the National Science Foundation grant DMS1206693 and NINDS grant R01- NS073671. Tiejun Tong’s research was supported by Hong Kong RGC grant HKBU202711, and Hong Kong Baptist University grants FRG2/11-12/110, FRG1/13-14/018, and FRG2/13-14/062. Lixing Zhu’s research was supported by Hong Kong RGC grant HKBU202810.
Link to Publisher's Edition
Dai, W., Ma, Y., Tong, T., & Zhu, L. (2015). Difference-based variance estimation in nonparametric regression with repeated measurement data. Journal of Statistical Planning and Inference, 163, 1-20. https://doi.org/10.1016/j.jspi.2015.02.010