Zheng, Shuzhuan Yang, Lijian Härdle, Wolfgang Karl
Year of Publication:
SFB 649 Discussion Paper No. 2011-002
Longitudinal data analysis is a central piece of statistics. The data are curves and they are observed at random locations. This makes the construction of a simultaneous confidence corridor (SCC) (confidence band) for the mean function a challenging task on both the theoretical and the practical side. Here we propose a method based on local linear smoothing that is implemented in the sparse (i.e., low number of nonzero coefficients) modelling situation. An SCC is constructed based on recent results obtained in applied probability theory. The precision and performance is demonstrated in a spectrum of simulations and applied to growth curve data. Technically speaking, our paper intensively uses recent insights into extreme value theory that are also employed to construct a shoal of confidence intervals (SCI).
longitudinal data confidence band Karhunen-Loève L2 representation local linear estimator extreme value double sum strong approximation