Simultaneous confidence bands for nonparametric regression with equal cluster size

Abstract

Repeated/clustered data are becoming increasingly popular in many research studies. While there is a considerable literature in the estimation of the nonparametric component functions, the problem has been addressed by very few in statistical inference such as simultaneous confidence bands (SCBs). Based on the efficient kernel estimation incorporating within‐cluster error correlation, we provide asymptotic Wald‐type‐based SCBs for the nonparametric function when the repeated measures have the equal cluster size. The performance of the SCBs is evaluated by simulation studies which support the asymptotic theory. The proposed method is also applied to a dataset on the Junior School Project of test scores.