Statistical Inference for Streamed Longitudinal Data

Summary Modern longitudinal data, for example from wearable devices, may consist of measurements biological signals on a fixed set participants at diverging number time-points. Traditional statistical methods are not equipped to handle the computational burden repeatedly analysing cumulatively growing dataset each time new data collected. We propose estimation and inference framework dynamic updating point estimates their standard errors along sequentially collected datasets with dependence, both within between datasets. The key technique is decomposition extended function vector quadratic constructed over cumulative into sum summary statistics batches. show how this can be recursively updated without need access whole dataset, resulting in computationally efficient streaming procedure minimal loss efficiency. prove consistency asymptotic normality our estimator as batches diverges, even independent remains fixed. Simulations demonstrate advantages approach traditional that assume independence Finally, we investigate relationship physical activity several diseases through analysis accelerometry National Health Nutrition Examination Survey.