Rejoinder: ‘Statistical inference for streamed longitudinal data’

Abstract

1 Introduction We thank the editorial board for organizing this discussion and giving us the opportunity to explore experts’ perspectives on our work. We sincerely appreciate the discussants for their insightful contributions, which have raised many important points and provided suggestions for potential improvements and generalizations of our proposed method. In this rejoinder, we primarily focus on three important aspects raised by the discussants: (i) the role of the weighting parameter in balancing bias and variance of our estimator, (ii) subsampling as an alternative method for improving computational efficiency and (iii) extension to high-dimensional settings. 2 Role of the weighting parameter We thank the authors of Song & Zhou (2023) for their important investigation of the statistical robustness properties of the quadratic inference function in our streaming longitudinal framework. In their discussion, the authors found evidence that our estimator is robust to low data contamination, regardless of the allocation scheme. Moreover, the estimator recovers quickly in the high contamination setting in the sense that estimation bias vanishes after a small number of batches. Inference patterns mirror estimation bias patterns, and so we focus our discussion on the latter.