Each week, we will be publishing layman’s abstracts of new articles from our prestigious portfolio of journals in statistics. The aim is to highlight the latest research to a broader audience in an accessible format.

The article featured today is from the Canadian Journal of Statistics, with the full article now available to read in Early View here.

Maiti, T., Safikhani, A. and Zhong, P.‐S. (2021), On uncertainty estimation in functional linear mixed models. Can J Statistics. https://doi.org/10.1002/cjs.11585

Functional data analysis is proved to be useful in many scientific applications such as Health Sciences, Biology, Economics, etc. The physical process is observed as curves on a sufficiently large number of grid points. In many applications, several curves are observed from multiple subjects, providing the replicates needed for proper statistical conclusions. The recent statistics literature develops several techniques for registering the curves and associated model estimation in regression frameworks. The standard regression models ignore heterogeneity among curves. The functional linear mixed model is one of the popular ways of combining several curves yet capturing variability among curves via random effects.

Although measuring the uncertainty is of paramount interest in any statistical prediction, there is no theoretically valid expression available for functional mixed-effects models. The accuracy of such valid expressions is important since, in real-life applications, only a finite number of curves can be observed, thus the lack of uncertainty assessment can potentially lead to an inaccurate decision. The main focus of this article is on measuring uncertainty in terms of mean squared errors when the functional linear mixed models are used for prediction. Specifically, a theoretically valid and bias-corrected approximation of uncertainty measurements for prediction is provided together with some modifications for model estimation. The proposed method is computationally simple. The empirical performance is investigated by numerical examples. Finally, the model is applied to two real-life examples, studying lung function and the effect of fibromyalgia (FM) through modeling blood concentrations of cortisol, respectively.