Difference-based Variance Estimation in Nonparametric Regression with Repeated Measurements

This work develop the difference-based estimators in the repeated measurements setting for nonparametric regression models. Three difference-based methods are proposed for the variance estimation under both balanced and unbalanced repeated measurements 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. Finally, two real data examples are analyzed to demonstrate the practical use of the proposed methods